Will caulking the cement pool to the cool cement deck allow the pool to fill up more so the water can reach the basket and pump so it does not suck air?

I have read your question several times an don't quite understand it. Do you have cracks or joints below the skimmer line? Hmmm. Just raise the water level until the water is at about the halfway point on the throat of the skimmer. It may be that your skimmer is installed too high. Don't know - would have to see situation.

Ken

After reading the original question posed I have a better understanding of the problem. Whoever changed the question didn't know what they were talking about. It appears, by the 1st question that you have some sort of problem getting water to the pump. As above, maintain water level at middle of skimmer. You may have to add water manually to the pump pot by removing the pump lid and adding water to fill the pot. Replace the lid and start the pump. It may take a couple of minutes for water to start flowing. As water flow increases, release the air entrapped in the filter, via the air relief valve at the top of the filter tank. Now, you have a "primed" pump and a functioning pool.