It should not but I have heard of folks who needed to do so by removing the output hose that goes to the A/C unit and run the pump till it pushes out water then reconnect the output hose.
Please shop around! There are high and low pricing for these pumps. Just make sure you get the same gph's rating on your pump. Gallons per hour. If you have trouble priming put the business end of a drynvac hose up to the output opening and suck the water out.
They do need to be primed. In many cases, the pump is low enough that displacement will flood the intake hose up to the pump when the seacock is open. In my 97 2800, that was not the case as the pump was placed above the water line.
I installed a Perko inlet connector just before the seawater strainer. It allowed me to connect a garden hose for priming, flushing and winterizing. i've opened the top of the seawater strainer and primed from there as well.
I remounted a new pump on my 2800 due to a new swim platform changing the attitude of the boat enough that it constantly needed to be reprimed. Simply lowering the pump mounting four inches solved this problem for good - believe me, you don't want the hassle of priming because varying conditions will have you doing that when you least want to. You also need to pay attention to the vertical pumping capacity of the pump. I found that by moving up one size from the original also ensured that water would make it to the forward AC unit in any set of conditions.