It'll handle them until the drag goes. I never met a Penn drag I liked until you get to the International price range.
Lots of better reels with nice smooth drags out there for trolling. Try a Diawa Sealine 50H If you can find one ($130 retail when they were still selling them). I've got 3 about 10 years old and they've never been apart or failed me. I don't believe they are made any more but you might find one floating around somewhere.
Lots of folks may argue about the Penns but I've owned them and used other folks recently. They aren't in the same class as a lot of other reels. SKspawner had a Shimano Calcutta 700 on the boat this weekend. Seemed like it was a nice reel for the job too but quite a bit more money.
I use mostely Penns primarily because of ease of getting them fixed, maintenance, etc. There is someone locally here in Depoe Bay who does a lot of the reel maintenance/repairs, and he does all of mine.
A 3/0-112 Senator works a bit better due to it's lighter weight but a 4/0-114 will work too, when used with spectra line. Penn has upgraded it's drag systems with SS washers and shouldn't have the problems Miss B is refering to any more.
Penn 4/0 - I have one - it wa my first sturgeon reel - don't like it much - very slow retrieve (1:2 or so). Also, the new drag washers are not nearly as good as the original, wich you cannot get any more because they were asbestos. However, that being said, if it's what you've got, fish it! Better than a spinning reel :grin: .