Whoops... Wasn't aware of that patch, sorry. But i can't imagine how copy/paste should work, because DOSBox uses graphics mode for output, not character mode, like the W9x DOS boxes, or NTVDM. There are no characters to copy, only pixels. (;
Ahh, i've read the patch desc, and i think i understand how that could work. Interesting idea. Dr.K.: if you want to try the patch, you have to compile your own DOSBox. The patch is quite old, so i think there could be compatibility problems with the current source (just a guess). I'm not aware of any "normal" build (like ykhwong's or Gulizoka's) that has the patch included.
EDIT: ah, and i think the answer to the OP's question would still be "no", even when using that patch. It's not for "standard" copy/paste, like we know it from Windows or other OS's, but for copying content to a specific device which acts as an interface to the windows clipboard (like the "copy clip:" functions in 4nt/tcmd32). I remember another thread on VOGONS about c/p, and i think there was another solution to the problem, something with an external program i think.