Good question! I tried mint.com a while back hoping I could use it for tracking some Girl Scout expenses - and no luck. As far as I could tell, you have to have it linked to financial institutions, there’s no way to have a “notional” account (i.e. one that exists only on paper).
As far as paychecks go, I would have to guess that there is - otherwise it pretty severely limits how useful it would be in tracking your whole financial picture. Quicken certainly does: you set up your paycheck once including breakouts for various categories (e.g. income tax, 401K withholding, etc.) - then set it up to “schedule” the deposits - biweekly, monthly or whatever. When you get your pay, you can either click once to enter it, or edit the amounts (e.g. if some figures vary from pay period to pay period). You’re not entering it from scratch each time, just correcting amounts.
Now you’ve got me curious!! I too find it limited, for some of the same reasons (several accounts won’t connect). And since I have desktop Quicken, the real reason to use Mint would be if I could enter stuff online while I’m out and about, and have it download to the desktop (like I used to with Pocket Quicken on the Palm Pilot). Intuit apparently has no intention of providing anything like that capability.
Where Mint can be useful is that it will send you alerts via email - e.g. I just noticed it sent me one saying a check deposit was officially available, I get reminders for some specific bills (if the financial institution tells them the due date, I think), and I get alerts for unusual spending.