Are there any negative consequences for taking too many turns in the final mission?

In the final mission, you must make it to the other end of a very large map to do your final battle.

There is no explicit turn timer on this mission. However, the in-game dialogue would suggest that there is a sense of urgency in completing your mission as quickly as possible.

Are there any negative consequences for taking a lot of turns before starting the very last fight at the end of the map?

If not, players could just use a bunch of idle turns in between each battle to reset cooldowns on abilities.

No, despite the sense of urgency you get from the voice comms, you can take your time as long as you want for the final mission.

This is somewhat like civilian rescue missions, where Bradford will constantly repeat "Commander, we are seeing HEAVY CASUALTIES" over and over despite only a few civilians dying. Granted, there is some urgency as you need at least 6 civilians but the voice comms have no impact on the mission itself.