Sort of.

The Synoptics as we have them today are from at least around 15-20 years after Paul's letters.

But particularly for Mark the picture is - as you said - a fair bit more complicated.

Not only is there the case for a proto-Mark, which complicates the post-70 CE dating given the key feature that depends on (the description of the fall of the temple) occurs in what's termed a Markan sandwich or didactic scene (basically where Jesus is expanding on something he just said publicly in a private conversation with only a handful). Was this a part of the original Mark, or was that scene a later interpolation bringing what was a statement about eventual impermanence of manmade things (Mark 13:1-2) in line with events that had then transpired?

Further complicating this picture is the relationship between Mark and Paul. While the simple assumption is that the author of Mark was familiar with Paul's letters (the case in Dykstra's Mark, Canonizer of Paul), considering this in light of a possible proto-Mark raises questions around certain curious language in Paul's letters.

For example, note 1 Cor 9:19

For though I am free with respect to all, I have made myself a slave to all, so that I might gain all the more.

Compare to Mark 10:43-44

But it is not so among you; instead, whoever wishes to become great among you must be your servant, and whoever wishes to be first among you must be slave of all.

One possibility here is that the author of Mark is seeking to place Paul in first place in the "who gets to sit next to Jesus" competition. But the specific language Paul uses of "in order to gain all the more" seems almost like he's actively employing the phrase knowing full well the implications.

This, in combination with his using the exact same forms of the Greek words for seed and sown seeds in 1 Cor 15:37-38 as the mustard seed parable in the Synoptics (itself related to the concept of bodily makeup by one of the sects declared heretical with overlapping concepts and sayings to elsewhere in Paul's Corinthian letters) has me inclined to think Paul had access to written sayings of Jesus at least some of which overlap with Mark.

So while I did go into the later composition and continued editing of the gospels in the comment above, the question of composition is an extremely murky one and the late first dating around the gospels commonly thrown around is pretty much hogwash when you dive more deeply into it outside of perhaps Matthew which seems the least to have suffered layers of redaction. Most of that composition is certainly after Paul, but perhaps not all of it.