The new AIP gives the SSK (NOTE) new endurance, not a whole lot more mobility! Yes, they can remain underwater for three to five weeks but, when a SSI leaves port, it has a finite amount of energy. It has X number of gallons of diesel fuel, Y amount of mega-watts in battery power and, Z amount of watts with AIP system. The captain has to use this wisely. This includes the sailing to the patrol area, patrolling and, returning. The primary task of the AIP is to recharge the batteries. The AIP provides a steady source of power. If the sub runs out of energy, it will need a tow back to port!
NOTE:
An SSK equip with AIP are now being designated (SSI).
Most SSKs can drain a fully charged battery pack in three to four hours at speeds above 15kts!! Then several hours would be needed to recharge the battery pack. The entire power package can be tied to the propulsion system to provide speeds up to 21-kts! But once this happens and the power from the batteries is drained, the sub must remain quiet until the batteries are recharged.
In answer to your question, yes the SSI can hamper the ability of a surface fleet. This is nothing new, for submarines have always had an advantage which required many destroyers to destroy or chase off a submarine. The submarine is the original stealth war machine.
The SSI will not replace the SSN but, it does provide a lot more flexibility to the navies that have them, in their ability to control their coastal waters. The SSK or SSI are great weapon systems for controlling choke points or coastlines to protect against enemy amphibious fleets. They are far less of a threat to carriers in the open ocean traveling at 25-kts plus. The new SSIs are getting as quiet as the best of the SSBNs! The SSBN is the sub where no expense is spared. Any submarine regardless of propulsion, has the 'hotel noises'. The noises of the sensors, lights, air conditioning, heating, and other necessary auxiliaries. These normally are in the order of 50-80 kilowatts (KW), continuously.
In an article, "Diesels or Nukes", by Robert A. Hamilton (originally published in the New London Day on Feb. 29, 2004). Hamilton quotes Lt. Cmdr. Todd Cloutier, "don't think of it as a very small SSN, it doesn't have the speed, it doesn't have the endurance, and it has counter-detection limitations." (The last point was not expanded upon!) "The biggest advantage, though, is to our taxpayers and their confidence in us."