When you just mount the possibly malicious USB stick and dont execute anything nothing should happen anyway. So you can safely mount it.
But if some malware gets executed this malware could (with root privileges) remount the drive and modify it (just like you could). But it is unlikely that it is intelligent enough to do so. It also coud modify BIOS and persist reboot that way.
So theoretically it might be possible that malware executes through a explloit in some program that accesses the USB drive. There is no additional security by using a usb live os, except from the (likely missing) intelligence to mount the drive.
You can't never be a 100% safe if you don't use a air gapped system and never attach anything to it (waht makes it useless for most cases)
If the malware does not uses an exploit in a program that is accessing the USB stick, you are fine without an additional live os. (Very likely)
If it does execute (very unlikely) and it is not programmed to mount the drives (likely) this live os helps, otherwise you have to hard unplug it.
If the malware gets executed and modifyes the BIOS, even that would not help.