Is my birth control fully functional after 2 month use??

Jillian • On Glow because I have a lot of things to worry about, and when my period starts is not one I have time for. ;)
I'm getting married on june 13th but the soonest i could get in with the gynecologist to start birth control is April 13th. Will i be safe to have sex june 13th, only 2 months away?? Or should he still wear a condom for the first month just in case? :P