The simple answer is - yes. Keeping water from getting through planking was essential in every part of the ship.
During the period you're talking about (the late eighteenth or early nineteenth century, I assume) the caulking probably would take the form of tarred oakum - a dark grey in color. The edges of each plank would be planed off at a slight angle, to create a groove for the caulking. The strip of caulking usually would be between half an inch and an inch wide. The caulking would show up on each side of each plank - including the ends.
In high-quality work (which usually characterized large British warships) the deck planks would be fastened to the beams with either wood treenails or metal bolts (depending on the period). In either case, the shipwright responsible for that part of the job would start by boring a hole (actually usually two holes, side by side)
halfway through each plank wherever it crossed a beam. The hole would be about an inch and a half in diameter. He would then switch to a smaller bit, (the same diameter of the fastening), center it in the hole, and drill the rest of the way through the plank and into the beam. Then he would pound the fasting through the plank and into the beam, leaving the head of the fastening countersunk below the surface. Next he stuffed some hot caulking into the hole and pounded in a wood plug, which was cut from the face grain of a board like the deck plank. When the caulking was dry the protruding part of the plug would be planed off flush.
The purpose of this ritual was to make the grain of the planks and the plugs identical, so that when the deck was scraped or holystoned the plugs and the planks would wear down at the same rate. For model building purposes, the point of all this is that the fastenings would show up in the form of hollow, dark grey circles - not the black spots one sometimes sees on models.
Whether all this is practical to reproduce on a model really depends on the scale. On small scales, a good, simple way to represent caulking is simply to run a fairly soft pencil around the edges of each plank. The pencil line will survive any sanding or scraping inflicted on the deck, and, to my eye at least, the color is just about right.
Hope this helps a little. Good luck.
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