I think it matters, at the lower 4 dance levels, what moves test the skater passed in determining the how quickly they progress in those pattern dance tests. At the higher pattern dance levels, I think it's more how hard they focus on the pattern dances while skating.
Yes, I personally think it's reasonable to pass Pre-Gold and Gold within 7-8 months if the skaters are determined to do it.
There are many skaters at our local rink who are focused on free skate (competitively or recreationally) from no test through senior level. When my daughter started taking pattern dance lessons on the side as a free skate competitor 7 years ago, she was the only one. Now about a dozen of them take pattern dance lessons on the side. Based on my daughter's experience and those I see around the rink, there's a huge variability in the amount of time taken to pass each level of the pattern dances. I can speak generally from observing them (including my daughter's progress & 2 of her close friends at the rink).
For those who passed senior moves when they started pattern dance lessons and compete in free skate, the first three levels (Prelim, Pre-Bronze, Bronze) were quick (most skate 5 days/week after school for maybe 2 hours/day on free skate, moves, & dance). Within 3 or 6 months of starting pattern dance lessons, those skaters can pass all dances forPrelim, Pre-Bronze, and Bronze. For Pre-Silver through Gold, the length of time gets longer and longer to pass all dances within that level.
My daughter was the quickest in passing the pattern dance tests amongst her friends. She was able to pass Pre-Silver within 3 months, Silver within 4 months, Pre-Gold within 6 months, and Gold within 9 months. This was all while she was still competing in free skate back then. My daughter started international pattern dance lessons 4 years ago and is almost done with those. However, she now only skates like once or twice a week so it's taking a while. My daughter's two free skate friends (Intermediate and Novice free skate level now & had passed senior moves at around age 13) appear to take a year at Pre-Silver and a year at Silver to pass all dances at those levels. They've been learning the Pre-Gold pattern dances for like a year now, and they are still practicing them, on the side, to eventually pass all 4 dances. Who knows how long they'll take to pass the Gold dances if they get to them.
I know several synchro skaters who were able pass the high-level pattern dances (Pre-Gold & Gold) in less than a year at each level by the end of their freshmen year in high school. They were focused, and pattern dance lesson is a requirement on their synchro team.
Good luck to your skater.