I use my entire pedal board in front of my Tone Port DI at times. At the very least, my Dime Distortion is usually in the signal chain as I like its sound a lot better than any of the modeled distortions or overdriven amp sounds available in POD Farm. As long as its output is instrument level, any effect you want to use should work fine. Don't know about the UX1, but my TP has a pad switch on it so it can handle higher level signals as well. I've used it with line outs, DI outs, and headphone outs on various amps with no problems.  I don't think I'd try it with a speaker output though. Matter of fact, now that I think about it, I've had my entire rig, complete with pedal board in front of the amp and rack effects in the loop to feed my TP. I just used the emulated speaker line out on my Randall to feed it and the pad switch to bring the signal down to an acceptable level. Bascially, it was a traditional setup with the TP in place of a mic'ed cabinet.

The only disadvantage to using front end amps, effects and processors is that if you decide you don't like something, you have to do a re-take. For serious recording, I setup my DAW to record the dry signal and basically just use the processed signal for monitoring while I play. Afterwards, I process the dry signal, adding and subtracting effects, models, etc. until my hearts content. If I can't get exactly what I want with the computer, I'll run the signal through external equipment and re-record the output. Provided you start with a decent sampling frequency, there is little signal degradation going digital to analog to analog amps/processors , and then back to digital. Additionally, the analog equipment provides more warmth and, imho, a better sound than a strictly digital setup.