I would have no problem recommending a Coaster that has surveyed in good condition for coastal use. They are reasonably good boats for that purpose. Assuming that the boat has been maintained in terms of rigging, and chainplate replacement, and that the wooden structural components have not rotted out behind the Formica, I would expect these boats to do fine in the kinds of conditions normally experienced by the typical coastal cruiser. While not as easy to handle in a blow as many more modern design, they are none the less reasonably seaworthy designs. If all you are doing is coastal cruising, you would not be expected to spend days at a time riding out gale force winds or being thrown from wave tops into the trough (as you might offshore) and so assuming the original structure is intact you should not have to beef things up. If it hasn't been done by prior owners, I would consider sounding out the decks for delamination and adding backing plates on the winches and major cleats.
The original mast supports were reasonably robust on the Pearsons. If the original mast support structure is intact and does not show signs of movement or deterioration, it is probably perfectly fine for coastal use.
The battery question comes down to several factors that you do not mention. If these are traditional lead/acid batteries you will need to be able to service them, and they should be in a vented compartment where the gases produced by charging cannot be ignited by sparks from the electrical system. The efficiency and durability of these batteries are also impaired by heat. Sealed batteries obviously do not have the same maintenance or explosion issue.
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Curmudgeon at Large- and rhinestone in the rough, sailing my Farr 11.6 on the Chesapeake Bay and part-time purveyor of marine supplies