Yes! Here in Sunny CA we get requests for boat art often.
One thing you failed to mention is how large is this piece and how is it framed?
On fiberglass: Check with 3M re: Command Adhesives. We have had good results with them but on TEAK there are other factors to consider, especially the oils David mentioned.
Teak is very light sensitive. There will definitely be a "fade" shadow on the wall when the picture is removed, especially if it is mounted permanently. We usually provide some type of removable feature so the piece is hung up when the people are on the boat. Then, we also have many who live aboard so they want it up all of the time. Is this a sail boat or a motor boat? If it is a sail boat, motion is much more of a factor.
Our experience with Teak is that it patches with filler or lacquer burn in sticks so well it is hard to see the hole.
My first recommendation is to attach industrial self-adhesive velcro pile to thin strips of acrylic (1/16 to 1/8" thick), then drill small holes in the acrylic through the velcro and lace the velcro to the acrylic with Tenera thread (now available from Attach EZ) or a type of thread used by sail makers. I would attach this to the bulkhead with small flat head stainless steel screws. The back of the picture would have Velcro Hook attached with both the adhesive and an additional fastener. If you use staples, they should be Monel or stainless.
Alternatively, I would not use glue, but would recommed a french cleat at the top and bottom with 4 small holes to attach them. A dab of silicone will hold the pieces together, but will allow for removability.
We have also used "flush mount" hangers that have a spring detent which allows for the piece to be removed for storage, but they are noisy and if the client is not careful, he will damage the wall by sliding the piece against the wall when installing and removing.
If you are using a metal frame (alumunim) be sure to use cast alumunum corner hardware and plastic springs (or filler board of coroplast.) Metal hardware will not last in a marine environment.