Hi Phil,
thanks for your question!
Yes, all you ask is possible.
You can trigger up to 4 different VSTi tracks with the Zaquencer, including drum racks.
When you´re happy with the tracks, you can record them as Midi in Ableton.
Too hook up the Zaquencer to a computer, you need a USB-Midi interface.
Such a separate USB-Midi Interface is often included in existing soundcards, or you can purchase separate, inexpensive interfaces for the upload. The cheapest one that we´ve found to work reliably is the M-Audio Midi Sport Uno, for example: http://www.thomann.de/de/maudio_midisport_uno.htm?gclid=CMGz3u2hhskCFQUOwwodh8EF5g
There are cheaper ones for around 5$ on eBay, but they are hit-and-miss, some work fine, some don´t.
Let me know if you have further questions!
Best,
Christian