Hello
No, there is no need to repot immediately. Gently knock the plant out of its container and check that the plant roots are healthy and not infested or dry and that the plant is not waterlogged. Pelargoniums should be watered and allowed to drain thoroughly, do not allow them to stand in water. Gently remove all faded blooms. After flowering feed the plant with 1/4 strength feed at each watering and when the roots start to appear in the holes at the bottom of the pot think about re-potting.
Ron

Thanks! I have been a bit alarmed, as when I moved it, I watered it well, and let it stand for 30 min., then poured off all the excess water and put it back on the window shelf.... and it is still soggy! (4-5 days later!) Seems maybe the soil it came in is too heavy?

This could well be the cause. Some of the new multipurpose composts, especially those based on bark and coir do retain too much moisture for pellies. If you have objections to using peat based composts try using a loam based compost such as John Innes No3. You could also try standing the pot on coarse gravel or chippings to improve drainage.
Hope this helps
Ron