Yes, a Men's size 11 boot falls squarely in the Large binding range, which typically covers US Men's 10–12. Large bindings are built with a wider heel cup and longer straps to properly secure bigger boots, so your foot sits correctly on the baseplate with no overhang.
If you size down to a Medium, you'll likely run into a few problems. The heel cup may pinch your boot, the straps might not reach comfortably across the top, and your boot could hang over the edges of the baseplate. That overhang can cause toe or heel drag when you carve, which catches in the snow and throws you off balance.
One thing to watch: sizing ranges aren't identical across brands. Always double-check the specific manufacturer's size chart before buying. Also, if your boots have a particularly bulky sole or inner volume, you might even find the Large feels snug — in that case, some riders move up to Extra Large for a more comfortable, secure fit.