I own a Spider V 20. It's a cute little bedroom amp and it's a lot of fun, and connecting the Stomp to it works pretty good.
So how good is it for an FRFR solution? That's hard to answer. My knee jerk reaction is to say "you get what you pay for" but if I do that I'm kind of selling it short a little because people tend to assume that that phrase means you get garbage with the Spider V, and that's not true. Especially the Spider 240 which is $500 . . . not exactly chump change. The Spider 240 is basically about the same clarity as my little 20, but with quite a bit more heft and oomph, and it's nice.
However, you're not just paying for the speaker. You're paying for all the modelling technology in it too. This means Line 6 packed in a decent flat response system, but not the best of the best for $500. Is it as good as a $500 Powercab that was largely designed to be a dedicated flat response? I personally don't think so.
If someone already had one and was looking to save money for a while, I'd say it's a great idea. In fact, there's a good chance you'll be happy for a very long while. If they didn't already have one, but wanted to save money, I'd steer them towards the Headrush FRFRs or recommend they get a Powercab. I wouldn't recommend they buy a Spider V for their flat response needs. Does that make sense?
Anyway, I hope that kind of explains where I think the sound falls. Better than a lot of options including a regular old traditional amp, but not as impressive as a dedicated flat response speaker system.
Edit: I also think the posters above were making connecting needlessly complicated. Yes, you can go through the auxiliary in, works great. You can also create a flat response preset and just plug in with your good old traditional 1/4 cable in the guitar in. Easy peasy.