Of course not. The blue player's turn should also be respected. There's no need to force them to take a turn just like that.

Kostya, as always, is concise and to the point, but for now, you can take a restart on someone else's turn:
"each player has the right to take a restart/restarts, i.e., start a new game with a map regeneration. You can take either 3 restarts on the first day of the game (111+111+111), or 2 restarts on the first and second days (111+112 or 112+111), or one restart on the third day (113)."
As we can see, it is not specifically stated on whose turn this can be done, but only the date is indicated, so legally, red has the right to take a restart on someone else's turn. In short, a small correction is needed, such as: "each player has the right to take a restart/restarts during their turn, i.e.,..."

Never mind.
Regarding your question:
Common sense suggests that no:
on the blue player's turn, many situations may arise, such as: turn duration; an open overview, from which a bunch of heroes suddenly appear for the opponent, or a sufficiently strong guard is broken, and much more, I just can't remember it right now.