Is the Jersey City Port Imperial parking garage likely to be full during the summer?

Port Imperial isn't in Jersey City, it's in Weehawken. Ferries to Manhattan run from multiple locations including Hoboken, Jersey City and Weehawken, additionally all these towns and the ferry terminals are connected with the Hudson-Bergen Light Rail; should you need to hop from one place to the other.

If you are willing to be flexible in terms of the places where you are willing to park, then you needn't worry. There are plenty of parking garages in Downtown Jersey City and Hoboken where you will be able to find parking and then take a ferry. (For completeness there is also the PATH system which connects both these places to Midtwon and Downtown Manhattan)

That said, I'm not sure why you'd want to park so close to Manhattan. Depending on where you are driving in from it may be more cost effective if you park at a NJ Transit Park and Ride station and take a train into Penn Station NY which is in Midtown. NJ Transit runs high speed trains that connects some of the NJ suburbs to Manhattan, most of these stations offer the Park and Ride option whereby you can park your car on the Parking Lot in the station and then take the train into the City. This is a good option because the traffic during peak hours on the roads into New York is almost always clogged up. While searching for a Park and Ride station be sure to check if it allows for overnight parking if you intend to leave your car there overnight.