Parallelizing dependent CI subjobs
The critical question is - can you teach your job #2 to patiently wait for job #1 to complete when it gets to that dependency point and appropriately proceed or bail depending on job #1 result?

If you can't, then the answer is no - you'll have more trouble dealing with #2 failures due to incomplete job #1, too much noise in the process.

If you can (and if you have enough resources) - yes, by all means - your process will be faster. You might not even need special support from the CI system for such dependencies, it could be completely oblivious, it would simply see the 2 jobs as parallel.

A middle-ground possibility, if your CI systems supports it, would be to stagger the jobs: start job #2 with a delay sufficient to bring the chances of job #1 completing before job #2 needs it in a much more comfortable range (say 99%). The delay would be plain eyeballed or empirically determined, either fixed or, in a more advanced approach, automatically derived from historic measurements/stats (if available).