You want to confirm that the counterfactual trends look parallel in treatment and control by looking at a random subset of the control group. There is little reason to believe that tells you anything about the treatment group if there is non-random selection into treatment. Suppose treatment group was on a different untreated trajectory than the control. Why would looking at the control group tell you anything about that?

The best you can do is test the trends assumption in pre-treatment data (if you have enough data to do this). If it looks good there, you might be more willing to believe it would hold in the counterfactual post-treatment data, but this is really an unverifiable assumption. There is no guarantee.

You might also consider using synthetic cohort and matrix completion methods that can relax the parallel trends assumptions.