Will a 5 string 34" scale bass be able to successfully handle the drop Ab tuning (AbEbAbDbGbBbEb)?

I'm a guitarist and i picked up a Yahama TRBX505 for some home recording because i needed a bass and I heard good things about it. I also wanted a 5 string because I was planning on buying a 7 string guitar and wanted to be ahead of the curve. After doing some additional research i've found out that a common practice for people who play 5 strings in a drop tuning typically have a longer scale bass like 35" and use a thicker gauge bottom B string like .140 or more. Currently the bass has a .130 bottom B. So i'm wondering if it was a mistake to purchase this bass at this point.

TLDR I just want to know if a 34" scale 5 string bass will be able to play a drop Ab tuning with good tension and support a thicker gauge bottom string.

Thanks!