Sure, why not?
All qualities can be graded.
Only adjectives that describe all-or-none properties like: present/ absent, dead/alive, true/false (in a logical sense), right/wrong etc. can only take a non-grading adverb like quite, clearly, absolutely etc., which does not grade the adjective but means 'undobtedly' or the like.
It is not clear what you mean by a 'quite/over critical task'. For example, in physics 'critical' has a particular meaning that can neither be graded nor intensified: critical mass/temperature etc. Adjectives can be gradable in one meaning and non-gradable in another, so we need to know the meaning of your adjective.
If a task is 'critical' when, if it is delayed, influences the finishing date, then the damage is variable and it can be gradable, as it is when it means 'expressing criticism'
@JoeBlow, in your comment there is a lot of confusion.
Arguably true, possibly true, previously true, ...., definitely true,
You do not seem able to distinguish between adverbs:
- 1) 'definitely' is equivalent of 'quite' (non-grading), and:
- 2) 'occasionally', 'previously' are temporal adverbs. Bottom line: none is a grading adverb, what/who is quite wrong?. Check here and with good a dictionary!