Works in theory, but...
If there was a "pause" button, everyone would hit it the instant the puzzle loaded, go off and solve the crypto on cheat sites or by hand, and then type as fast as possible to get all sorts of quick times.
Your slow time won't affect the average. The solve rates and average times are fixed when the stats are first loaded in. I figured that out by some memorable quotes whose times and rates never changed, no matter how many times I solved it.
My best suggestion is to leave the site from your "recent games" page, after waiting at least two minutes after the last puzzle to make sure all are visible. Some players wait ten minutes, just to be extra sure.
Slotted spoons don't hold much soup. - Stephen Sondheim