No, because that defies the whole concept of survival. Survival is another word for puzzle rush with infinite time. If you wanted to make a time limit, add another gamemode, but dont remove survival. Also, likes don't really do anything.
Are my puzzle rush scores good for my rating?

3 min - 20
5min - 24
survival - 35
rating - 700 rapid
After spending like an hour on survival i finally got higher score then my five min. Survival allmost seems to have harder puzzles, but maybe its just the extreme focus during the limited time.

On this account I think I reached the following stats:
- Puzzle rush 3 min - 30
- Puzzle rush 5 min - none (I didn't play)
- Puzzle rush survival - 49 (highest) (that's because I intentionally get it wrong after 49, even if I know the solution, as untitled players are not shown in the leaderboard, if they score over 49). On another account I reached 56 as my highest score in this category
- Bullet - I don't play
- Blitz - I don't play
- Rapid: I think on this account I am somewhere around 1500+, but on other accounts I got to 1900+. Truth being told I guess I'm just a high 1700 (as I refused all my life to learn openings and I just play based on instinct and power of analysis).
- Puzzle rating: on this account I think I'm around 2500+, but on other accounts I got to 2700+ ( which in no shape or form reflects my ELO )
y = 40x + 520
y = blitz rating
x = puzzle rush 5 min highscore
That's based on my friends' scores on chess.com
This is actually roughly accurate
3 min: 31
5 min: 35
survival: 54
puzzles: 2651
blitz: 1084
bullet: don't play
rapid: 1463
the truth hurts: -836
i.e. 1084 = 40x + 520 = 40 * 35 + 520 = 1920 + the_truth_hurts
y = 40x + 520
y = blitz rating
x = puzzle rush 5 min highscore
That's based on my friends' scores on chess.com
Than I would be at around 1600 bullet rating, and I suck in bullet

y = 40x + 520
y = blitz rating
x = puzzle rush 5 min highscore
That's based on my friends' scores on chess.com
Welp that would mean that my rating would be 2130 but I am 100 rating points above that
x = 29 but it was a survival that took 4 mins 30 secs
blitz is 244 for me because i'm new
so I would be... 1680...?

Survival 40 / 5min 30 / 3min 26 | But I don't know why does chess.com shows my best scores as Suvival 35 / 5min 29 / 3min 20 ???? There is a bug :\

chesscom survival: 51
5 min: 43 (Top 3 Scores 39, 40, 43) I got 39 like 5+ times and it took me almost a year to get from 39 to 40, then a week to 43)
3 min: 35 (37 in puzzle battle)
2794 peak puzzles
1600 puzzle battle
1243 peak blitz
1266 peak rapid
1129 peak bullet
Lichess: +22 puzzles in 90 seconds or 69 on puzzle racer, 39 Puzzle Storm , 2222+ Peak Puzzles
1669 bullet
1644 blitz
1732 Rapid
Playing for maybe 8-9 years
My best puzzle rush survival is 42 which I got just now, my rapid rating is around 1050, I have never tried 3 min or 5 min puzzle rush my bullet is 350 my blitz is 600 and my puzzles is 1800 and I am currently on a 8 correct streak