Both of the "original" Phattys (I have the Slim currently) have a HUGE MIDI implementation capability.
If you'll dig deep into manuals for your LP (be sure to download all the latest updates from the Moog web site), you'll find all the details for the paramaters that can be controlled via MIDI. Virtually every hardware control on the panel - and a whole lot more - can be controlled via MIDI!
What you DO with all that MIDI control depends a lot on how MIDI automation is implemented in your particular DAW, and just as importantly, how much effort you're willing to put into it to learn it.
Short answer, YES - you can definitely do what you want to do with a Little Phatty using MIDI inside a DAW. And while using a VST plugin would probably make it MUCH easier to automate the MIDI inside a DAW, it's not absolutely necessary. Unfortunately, the VST for the LP/SP (developed by a 3rd party) doesn't have a real good reputation, at least based on what I've read on the forum. I use the stand-alone Librarian, which seems to work fine, but don't have any "hands on" experience with the VST plugin.
Concerning VST's (and plugins in general)~
They're generally compatible with a LOT of different DAW packages. A few DAWS have proprietary plugin formats, and there are some variations between Windows and Mac platforms, but the documentation for your particular DAW will let you know up front which plugins will work with it. The VST plugin format is definitely one of the more common, and works with a lot of DAWS.
BTW -
If you're an iPad user, there are plenty of apps available that can give you essentially the same level of control over your LP as a full-fledged computer-based DAW, just in a MUCH lighter package!
Good luck with your project!
Randy
Little Phatty Solar CV, Minitaur, Slim Phatty (x2), MF-101, MF-102, MF-103, MF-104M, MF-105M, MF-108M, CP-251 (x2), Animoog app, Filtatron app, Model D app, Model 15 app...and some 5U modular and Doepfer stuff...