Your problem is not going to be the bulkhead. Round headed machine screws through metal backing plates
on each side of 1/2" ply with nuts squeezing it all together so the threaded ends of the bolts become studs will be more than strong enuff to carry the weight of any TV I can think of.
Shim out the mirror to accommodate the bolt heads.
HOWEVER: The "arm" that is part of what you say you intend to use will be far, far from able to carry the weight of even a moderately heavy TV in any kind of weather
when the boat rolls and pitches. When alongside or at anchor
it may suffice, but if you are going to accept such a restriction you still have to ensure that the TV itself can be secured to the bulkhead itself (taking the weight off the arm) so the arm doesn't have carry the very considerable forces of acceleration and deceleration that will be generated in a seaway.
As MySaintedMother was wont to council me: "Build it so it can take the weight of a well-grown man thrown against it in a seaway!"
All the best