So the vent off the 2" tub drain line runs up parallel to the main stack, and exits the tub drain line right near the main stack?
Is there any opportunity to put a vent on the tub drain line closer to the P trap and then up and over to the existing vent?
If the vent is too far away, theoretically it won't do its job to keep the water in the trap from being sucked out, and the tub may drain more slowly.
If the tub drain is close to a framed wall, which I presume logically it must be, you might be able to trench over to the framed wall and bring a new vent line up and then over to tie into the current vent. I don't think there's an issue with having two vents off the one drain line.
All that being said, no harm in putting the pipes together the way you want (glued) and putting a big funnel on the P trap. Then run water into it with a hose or buckets to see how well it drains and if the trap remains full of water afterwards, as it should. If so, and if no plans for a measuring-tape carrying inspector, as was said, keep on trucking!
You want to make sure it all works well before pouring concrete of course