Can bacteria in plates placed in the refrigerator still grow?

Yes, of course. The 4 degree environment only inhibits and slows down the growth of E. coli to a certain extent, when you take the plate out and put it in the right environment, E. coli will continue to grow, I once forgot to adjust the incubator temperature after coating the plate, put the plate in 28 degree overnight and found that the board has no point, but after adjusting the temperature I can still see colony generation. However, it provided that your vector and gene successfully connected and transformed.