Quick rundown on that doctrine for anyone interested.
It has a synopsis of cases where it has been applied either to deny or allow such appeals. If one of these exceptions somehow applies to this, I'm not seeing it.
Here's one on a vaguely related issue:
A SLAPP claim differs from this in that SLAPP confers something much more akin to an immunity (like qualified immunity) from suit than the denial of a motion for summary judgment, that is to say, the harm of a denial of the motion is a denial of
the right not to have to stand trial at all. Unless this Colorado SLAPP statute applies, though, such a right does not exist, so neither would a right to appeal.
That's sort of an ouroboros but if the court doesn't even have jurisdiction at all, it should be treated simply as the denial of a motion to dismiss or summary judgment. So I don't see the court even getting there unless it either falls into the collateral-order doctrine exception (not seeing it) or some other extraordinary exception (fat chance).