I have a couple of SYN2's with several modules and have run them a couple of different ways.
It really depends on what your goals are.
If you're trying to get as close as you can to the actual amp in both sound and feel your best bet is to run the Synergy through at least the same brand or series of amp. For instance my Savage and Powerball sound and feel that much closer to the real thing when going through my ENGL inferno or Morse. Same with my IICP module. Going through my Mark III I get closer to the full Mark series experience.
If your goal is a 98-99% approximation to the real deal amp with a solid feel then going through a power amp that already has a solid foundation and feel that you like with will get you there. If you're running the module through a wimpy, thin power amp that's what you're going to get. If you have it going though a solid power amp with a lot of balls you'll get that experience. As far as the sound influence, yes the power amp will affect that as well. Whether it's a good match for the module is subjective. You may not like an 800 module going through 6L6's. Then again it may be your new favorite mix and match combo.
A third option is to run modules through a Fryette PowerStation. That's one of the power amps they test modules with. I've been using my SYN2's mostly with my PS100. I think this gives you the best balance when dealing with multiple modules. This has the module doing the heavy lifting on tone with the PowerStation having minimal influence in that regard. You'll be closer to the actual amp verses using a different power amp than what's usually associated with it. The PS100 has enough controls to let you dial in the balls and brightness to your liking. In most cases you can get at least into the infield with that. Feel wise I'd call it neutral. There's some give to it but it's not overly saggy. There's also some tightness to it but nowhere near being sterile. Like I said, pretty neutral to be a good balance.
A final option that to me is up there with the PS100 is using an upgraded Randall RM100. Foglifter and dual channel mod is a must if using Synergy modules. You get an even better experience adding on the NFB mod and Mercury transformers/choke. Granted, even if you get a RM100 on the cheap the mods are not really cost effective. I was able to score a fully modded RM100 for less than the cost of the transformers. If you do happen to come across a RM100 with Mercury transformers grab it. It's definitely worth having if you start going down the Synergy/MTS rabbit hole.