Yes. When I do this, my recirc arm is a piece of loc-line and I jump from in to outside of the hop spider when chilling or I'll get stratification of temps inside the spider. My spider doesn't cover the whole tun like a lot of folks. Mine is about 6 gallons big in a 17 gal tun.
I'm thinking of making mine smaller. Also, I do get an overflow when I try to recirc entirely in the spider.