Is there any established system for evaluating positions taking into account time for both players?
No, there isn't. This is for two main reasons:
- There is no objective measure for how time affects a player's ability to play any given position.
- Such evaluations would be useless. They would literally tell you nothing useful
Let me give an example from a game one of my clubmates (rated about 1800 at the time) played a few years ago in the UK National Universities Championships.
In the blitz section (3+2) in one of his games he reached a KBN vs K endgame with less than 30 seconds left on the clock. He knows that endgame (he has a strict coach who makes him learn that kind of stuff) and so blitzed out the win with plenty of time to spare on his clock.
I also have stronger clubmates (2100+), however, who don't know that endgame. They would never be able to mate in so little time. Give them 20 minutes on the clock and maybe they'd succeed. There have even been IMs who have failed with plenty of time on the clock.
Bottom line: even with as simple a position as this there is no way to provide a meaningful evaluation of the position that takes time into consideration.