You most certainly can record off the external instrument in Ableton! Although I don't use my virus this way, my Nord Rack 3 works charmingly well. If you do it this way, you'll most likely need some sort of midi interface though (Unless you're just plugging your keyboard straight into the unit). I bought something super cheap and it works incredibly well
http://www.roland.com/products/en/UM-ONE/
If you have multiple hardware units you might want to spend a bit more, as this is only good for one synth at a time kind of deal.