It depends.....the thing that makes helo dipping sonar so effective is that once it detects you, it can be moved quickly and efficiently to lay in your course, speed, etc while hovering rather than passing over you repeatedly. Typically the helos don't just happen upon you......there's been some clue that you're out and about and they're out trying to find you, along a bearing they have some clues about, etc. occasionally an air asset will spot a scope or, more likely, the wake the scope generates on the surface (modern surface search radar can also detect a mast and its wake).

Finding a submarine is still tedious work, and a UAV might be more suited to such work as it doesn't get bored, tired or distracted talking about that communications chick that's banging everyone onboard, or the latest scandal involving married crew members x and y's torrid affair, or even the latest sports scores. It is single-minded in methodology and execution, which would probably make it fairly effective.

Admittedly though, I have been out of the Navy for almost 8 years and off of submarines for 10, and UAVs were just coming online with a serious purpose in active war fighting then. I was also an enlisted nuc, rather than an officer.....but in addition to my engineering department duties I was a part of the ship's section tracking party (helping track contacts, plot firing solutions, etc), helped plan TLAM strike packages and worked in the torpedo room during battlestations-missile, including during actual strikes on station in 2003. So I'm not an expert, but I did get a broad base of experience outside of my NEC.

How would it change doctrine? I'm not really sure. The advantage still lies with the submarine, given the ranges at which they can engage surface ships and slink away. The oceans are large and deep, and for the foreseeable future I'd rather be under the ocean rather than on top of it if it came to war.