Can a DJS-1000 receive MIDI data from the DJM-S11's USB port?

short answer: yes, but...

the DJS-1000 can send/receive Midi data via USB (USB B port). the DJM-S11 can send (but not receive) Midi data via its USB B port. so yes, the s11 can send midi info to the DJS.

less short answer: no, not directly, but...

Midi over USB is fairly easy to setup when connecting USB Midi capable hardware devices (eg. with USB B ports, occasionally USB Micro/Mini ports, and more recently USB C ports) to a computer running a DAW, soft synth, etc. In order to connect between just hardware devices via USB Midi you would need a USB Midi Host (eg. Kenton MidiHost, Retrokits RK-006, Raspberry Pi). so you can't connect the DJS and s11 with a single USB cable but with a midi host, you could connect them using two usb cables in order for them to communicate via Midi. 

long and incomplete answer: once you have the s11 sending Midi info to the DJS-1000, you need to match up the Midi Out of the S11 with the possible Midi In that the DJS receives. I don't own an S11 but I do own a few DJS-1000s and a ton of midi controllers many of which have been mapped at various times to the DJS-1000 in some useful (but sometimes useless but interesting) ways. but glancing at the S11 List of Midi messages doc, i would be surprised if one could find a useful mapping allowing the s11 to do much of anything of use to the DJS-1000 - but check it out for yourself using the List of Midi messages for the s11 and the Midi Implementation Chart for the DJS-1000 on the links below: 

https://www.pioneerdj.com/-/media/pioneerdj/downloads/midi-mapping/djm-s11/djm-s11_midi_message_v100_e.pdf

https://docs.pioneerdj.com/Manuals/DJS_1000_DRI1489A_manual/?page=52

Unsatisfying answer: While you could get something like a BomeBox and re-map the s11 to the DJS-1000, you'd probably have a much happier life just picking up something like the FaderFox EC4 (compact, midi mappable, usb midi and din midi, etc.) to control the DJS-1000.

Totally helpful - thank you. 

Let me try this one...can I send only sync data, just detected BPM from any general audio input signal (no control data), via midi, this time from the USB port on a DJM-750 mkII to the same DJS-1000?

I'm looking for a way to automatically sync the DJS-1000 to the BPM playing on vinyl records, played through a Pioneer mixer (that isn't a 900NXS2). 

Or could i use a cable like the Roland UM One that goes from USB-A to standard MIDI 5 pin, to transmit BPM data?  Do Pioneer mixers only send MIDI data via the USB B connection?  Is there such thing as a USB B to USB B cable?

The DJM-750MK2 does send Midi clock via the USB B port (though not transport controls like Start/Stop). The DJM has both USB and DIN but whichever you choose, you'll need a Midi Host (or a computer) to translate the USB midi from the 750mk2 into a receivable Midi Clock signal via USB or DIN for the DJS.

so to answer your questions: 1) No, you can't use the Roland UM One or similar because it's not a Midi HOST, just a Midi INTERFACE (ie. allows you to send Din Midi into your computer for DAWs and such) 

2) Some Pioneer DJ mixers send Midi via 5 pin Midi ports and/or USB, but I can't think of any DJM that receives and can be 'slaved' to Midi Clock (for the obvious reasons). 

3) USB B to USB B - lol i actually tried this idea when i first got my DJS (and didn't know anything about Midi Hosts). it didn't work. if you want to know why, there are long and depressing articles online about why this doesn't work. 
Midi Hosts run from about $50 to $200 depending on how fancy you want to get. You can also make a super simple USB Midi Host with a raspberry pi 3 or 4 (each has four USB A ports so there you go), though at the moment they are not super easy to buy. 

so after explaining how you can sunc DJS to DJM via Midi clock, here's why it's a bad idea: 
Based on experience with the 750mk2 and a few other DJM mixers, while Pioneer DJ's DJM Beat Detector is almost always dead on in the case of non-PRO LINK sources (sources like vinyl records, CDs, etc., though for reasons I will never comprehend Pioneer caps the upper end of Beat Detector at 180bpm) using this BPM via Midi Clock being sent by the DJM can be frustrating since the BPM can get manually changed or temporarily misreported, and if you have the DJS in Midi sync (in) mode you can't use Nudge or the pitch control. 

There's actual good news here: depending on how you have your DJS setup, the DJS has an internal beat detector which you can use to match the DJS's BPM to vinyl. you still have to manually press a button on the screen, but it is accurate. You would have to have the mk2 SEND set up (1/4" to 1/4" to send back to the DJS (INPUT on DJS), but if you've ever used the Live SAMPLING feature, then that's all you need to setup.  Watch this video for an in depth tutorial on doing this: https://youtu.be/wcemqb2ORCE 

Good Stuff - Thanks. 

Yes, I've worked with that last suggestion - running sends from the mixer, to the DJS's inputs and using it's own onboard tempo detection.  That seems to work best and like you mention, still allows for tempo bend and adjusting.  I used it also to grab loops live.  But at that point, the mixer's Roll effect can work in a pinch (but that drifts a little also).  I enjoy the loose, live nature the DJS brings to the table, just sometimes it gets too loose.

I also agree, the 750's tempo detection can often 2x or 1/2 time the BPM, especially working with wonky, old vinyl.  This could be a disaster for the DJS.  I love my 750 and it's been the hub of many set-ups - digital and analog but I may break down and try Denon's x1850, which includes din MIDI out.