Ah, the eternal conundrum - do we strive for as fast a time as we can or move with the best form we are capable of?
I’m gonna shamelessly steal from Coach Glassman here and say “YES”
With functional movements, good form isn’t good because it’s pretty, it’s good because it is efficient. Effort spent on maintaining proper mechanics will be rewarded by faster times as your effort actually achieves what you meant it to do.
The other thing folks normally think about bundled with form is range of movement or ROM. This is really not optional as shortened movements mean you are not doing the workout prescribed so your time is DNF.
It is a given that form will deteriorate once you get tired, this is where a coach should earn their money. For those without access to a coach try recording your workouts on a digital video camera (many cell phones have this capability now). At first, try and compare the video of you to any one of the many available demonstration vids you can find on the net. Once you have got as close as you can, post something up here so we can help you to the next stage.