Ultimately yes, going back to Proto-Indo-European *pet- "to rush; to fly".
This is the source of such words as ποταμός "stream, river"; πετώ "to fly, to throw"; πέφτω "to fall"; φτερό "feather" and φτερούγα "wing". (The latter three were πίπτω, πτερόν and πτερυξ in Ancient Greek, with πτ.)
I think πτήση "flight" is related to πετώ "to fly" but only more distantly to those others ("fall", "feather", etc.).
English "feather" is also from this same PIE root, by the way.
I was pretty sure too that πετώ had derived from ίπταμαι. So I did a bit of research, just to satisfy my own curiosity, and found that πετώ was πέτομαι in the ancient times. ἵπταμαι appeared during the Hellenistic Era, at which time πέτομαι had already become πετῶ :-)
But, for instance, in this throughout answer you gave: Did you actually bother to do a little research only to answer me, or you already knew (at least most of) that by heart?
I assumed that πτήση and πετώ are related. And I think the Ancient Greek form of the latter verb was ίπταμαι (but I can't find that offhand so I may be misremembering).
I had wondered whether πτώση "fall" was related but thought that unlikely and was a bit surprised to learn that the family included not just πτήση, πτώση, φτερό but even ποταμός.
So, I'd say about 80% of my answer was a little research just to answer you. (And because I was curious as well.)