Probably yeah.
(am gonna use European standards here sorry Ameribruvs.)
Also, 200w bulbs that fit into fridge socket? The "40w max" is usually in normal E27 sockets. (The regular light bulb socket.) And the largest lamps for those I've seen are around 50-80w, and pretty much always sold as "growlamps".
Going to 200w you'd need an E40 socket. They're about twice the size of the "regular" E27 (and E14 is the smaller "candle" socket, that's like half the diameter of the regular one). Here's what a 200w bulb looks like and remember that the socket is twice the size of a regular one. That bulb is like ~40cm long.
Idk what socket fridges use though, but I seriously doubt it's anything close to an E40 size.