Is there any benefit in disabling wifi on my Mac Pro (connected to a time capsule via ethernet)?
I notice that with it disabled airdrop doesn't work and iTunes wireless sync misbehaves.
The benefit is, well, these other services will work. The drawback is another active network interface, increased chatter on your local network, and a few extra watts blasting at you.
That said, there are a few things that can be done to minimize the disruption.
Personally I find AirDrop to be totally useless when Messages can do everything better: it can easily transfer files over Bonjour with another Mac running not just ML's Messages but also iChat. My office of 60ish users rely on iChat (and now Messages) enough to where "to iChat" has become verbified around here. AirDrop is 10.8 only.
Also, Messages can be set to auto-accept incoming file transfers, look in Preferences > Alerts, change the Event to Incoming file transfer, check the Run AppleScript box and choose the Auto Accept default. AirDrop has no such options.
iTunes wifi synch definitely works best if the Mac's wifi is on, but I don't think wi-fi synch is particularly useful; I'd rather have a faster synch that uses less battery life.
Finally, AirPlay quality depends on many factors, such as your network hardware, signal strength, interference, and the remote devices. Both my 2nd-gen AirPort Express and then my Philips Fidelio AD7000 would stutter and drop off my mixed b/g network from my Linksys WRT350N - until I replaced its firmware with DD-WRT. Since then both have worked flawlessly. Your mileage, of course, may vary.
but will it affect speed of LAN transfers?
Well, you can choose which one would be preferred (by dragging it to the top in the Network preference panel):
As far as I know you cannot get a FASTER transfer by using both at once...