Is There A Way To Repair Concrete Steps That Are Crumbling Without Removing The Steps To Do So?

I have actually done this myself.
It depends on how badly the steps are crumbling. If they are really bad, then I'd say demolish them and start over, but if they're not too bad it can be done.
You will need to use a concrete, (patcher) material, not just regular concrete because regular concrete will not adhere to the old concrete.
Sakrete makes an excellent concrete patcher and it is quick drying.
  If the steps are crumbling around the edges, you may have to form them up with plywood in order to get the edges nice and straight. Once it sets up, just remove the wood.

Since we don't have any idea what conditions your stairs are, or the extent of the repair required, it is really difficult to give any advice. Post a picture if you can. If it is on the verge of collapse, leaning noticeably, or there is large separation...then you're better off building a new one. That may not be something you want to tackle by yourself. If it's only surface spalling, or crumbled edges, you can clean the area and repatch like the others have suggested. (See the attached sketch.)    ~ If you wish to dress it up a bit, and to hide the repair, you can always add some outdoor tiles to the treads (and even the risers if you are ambitious) after the base repair is done. Just make sure they have a rough surface for the wet weather. You can also use slate or stone tiles. Of course, it you live where there is constant freezing and thawing, then just forget it. Just move south where the sun welcomes you everyday.  : )

There may be better way to do in than I did, but I simply made sure steps were dry and clean before I began and built frames to enclose the repair areas.  I think it may also depend on how large the damaged area is.  I had some luck with patching a 1' x 1 ft piece, and also, in repairing a separation of porch steps from porch where settling had occurred, but used the best quality concrete I could find based on a contractor's suggestion, who also instructed me to ensure the concrete was not over diluted in mxing.  It's lasted now 8 years with no crumbling, which I think is the most prevalent problem when patching and repairing.  The contractor also told me he wouldn't suggest doing large pieces (like 1/2 of a missing step 8' x 1' x 8", because if the bond near the old portion  fails, the entire step then needs to be replaced.

I would say that you would have to do that is stages and build it up, but even then, I don't know that it would really work that well, let alone stay together. How about talking to a company that does a lot of this repair work.

I have seen it done and it turned out better than I thought it would, and it held up but the contractor is the key.  Finding the right guy is very difficult.
Would bricking the treads (or maybe risers too) be an option?

Nomad! If it's crumbling then you mixture didn't have enough "Fly Ash" in it! It is a Hardener because!
Tear it out and reinforce with re-bar across! First the bottom cross bars! Then while it's still real fresh stick re-bar up and down or tie it all and tap it lightly with a small hammer setting in the re-bar! Now it is strong and won't ever crumble again!