Can discrete wavelet transform for denoising purposes be implemented in real time?
Even though I'm not much of a wavelet expert, I can answer with a definitive YES!!
Now, do you have any messy details to complain about, like the size of the box, the power that it consumes, or the number of frames of delay between the taking of the image and its display?  Because that's your real problem.
Take the particular wavelet transform you want to use.  Sit down and with pencil and paper figure out how many calculations (floating point operations, basically multiplies and adds) that need to be performed per frame.  Look to see if the transform you want to use works with the fast wavelet transform.  Multiply the FLOP per frame by your frame rate -- you should have an answer in MFLOPS or GFLOPS.  Now hold that up against available processors or FPGAs, and figure out what needs to be in your box.  Then multiply by three, because it always takes more real estate to do a calculation than you think.