Can I run a dehumidifier pump to a washer stand pipe?
Yes, there should be no problem with doing that, provided you're within distance constraints of the pump. The washer stand pipe should just be a vertical pipe, with your washer drain going inside it, and not actually connected/sealed. This is done so that there is a vacuum break. You should simply put the pipe from this pump along side the washer pipe in the same way - do not attach it with fittings, otherwise you risk water from the pump going into your washer, or more likely, drain water from the washer going into the pump. 



In this picture, the white pipe is the standpipe, the black is the drain connected to the washer.

Basically, just put the pipe from your dehumidifier pump alongside the black pipe.

To echo @Jeff Widmer, you may want to tie the pipes down afterwards (a zip tie or some electrical tape around the whole thing may work), just to be sure neither pipe ever slips out and sprays everywhere. Again, don't seal this up or use fittings - you specifically need an air gap.