Hi Charlie,
I have heard of using dish soap in bottom trays, but diluted by water. I do not recall a discussion using pure dish washing soap. One problem folks mentioned when using the diluted version is evaporation.. With this in mind I do not know how fast the pure soap evaporates. Just curious; If or when it does evaporate, what will be left behind in the tray?
Now, since your bees can't reach the tray or it contents in any form, I do not see an immediate problem as far as contact goes. As far as odor or any other problem you ask about, I do not know. I look forward to hearing from others on this.
Good Topic Charlie. Thanks for posting.
Phillip