You can mount on a carpeted board, but like
@Ronnie says, you need cooling behind the amp, so you want to stand it off the board to allow for cooling if it is carpeted. The XD or M 700/5 JL amp has feet that stands it off a board or backing but the carpet blocks it without some standoffs. I actually just added two nuts on the threads exiting the board, to allow the feet on the amp to set 1/4" off the carpet and that is sufficient.
Some have mounted the amp directly to the wall that the setbacks attach to, and others have mounted it to the wall that is under the helm instruments, but you will need a surface to attach all the wiring to provide strain relief and that is a main reason for mounting to a board, because you will have multiple attachments to the board for strain relief of the cabling and wiring. I think you have the Clarion HU/remote, and if it is working, that is sufficient and the 700/5 will add good power to your existing speakers. But if you don't have the Polk db651's (a speaker Yamaha went to for stock but don't know when), and instead the Seaworthy 100W (max), they won't last long, as it is a paper speaker. But the db is a great entry level speaker and will provide years of service life even if amplified.
You will probably have to "extend" the stock speaker wires if you use them (I did and will again), which means cutting them from the connector and soldering (and insulating)an extension to them so you can reach the amp with them. Otherwise, you have to run new speaker wire to each speaker in the boat.
Leave yourself about 5' of all the cable/wire that connects to the amp, so that you can remove the 4 connecting bolts or screws and pull the amp out of the compartment to make adjustments. The same with how you strain relief the wiring and cables, make it easy so you can cut tie wraps and get it out, and easy to reattach them.
You will love that amp, very efficient and clean!
