Can I delete the system and application files on old MBP 2009 hard drive and still access the files in users?
I wouldn't put much faith in an 11-year-old drive, long-term. I certainly wouldn't put the only copy of any data on it.
That said, so long as you never expect to boot from it again*, then the old System files are just waste space, deleting them would be harmless.
It wouldn't, however, give you any speed increase, merely more free space.
Old 'spinny rust' hard drives are maybe 20 times slower than a modern SSD - even assuming a fast drive for its age, full SATA III support &amp; a full-spec USB3 enclosure.
*Not that a drive from a 2009 Mac would have an OS that the current Mac could boot from, even if it was completely up to date before you removed it from the old Mac