Can you run a real pedal with sims?

Sure, I do it all the time. You won't damage anything, if that's what you are asking. Tubescreamers work great for this, but I even run distortion pedals into my DI into DAW sometimes too.
 
Thanks for the responses.

Ok, so I borrowed a pedal just to try this out. What I found interesting was that using the real pedal got rid of this certain quality to my sim tones that had been bugging me for awhile. It's hard to describe, but it's that certain sound that amp sims combined with tube screamer sims give off. That certain thin/hollow fake sound, really don't know how else to describe.

So anyways, looks like I'm in the market for a new tube screamer pedal. My question is, for those who have used them before, are those ts pedals with actual tubes in them in any way a significant improvement over the old stand-by Ibby ts? I've hit Youtube looking for comparison vid but mot of them either sound bad or the stuff being played in them are all blues licks.