I did turn Time Machine off several days ago (1st time in 10 years) and turned it on today to have a fresh back up before the upgrade.
Turning off the backup is not a good idea.
You are not actually creating a fresh backup. When you turn it back on Time Machine will simply do a major check of every file vs what is in the backup. In a way this is good thing.. but as Bob indicated, if you have a slow wireless link it is very slow and inefficient.
The best way to prepare for an upgrade is to create a bootable clone on a USB drive. On a really old Mac like yours a FW800 drive would be even better. I forget if you have USB3 ports but USB2 are a fair bit slower than FW800.
I recommend you download Carbon Copy Cloner. It is free to use for a month.
Create a bootable clone to USB drive of equal size or bigger than one in the Mac. And then do actually boot from it. The big advantage of a clone is you can check everything is there.. your music, your emails, your documents. Test all your websites and their passwords are working. It should work exactly as your internal drive.. except it will be a fair bit slower of course.
Then you can run the update knowing if anything goes wrong you can instantly recover.
Time Machine is just not as easy or reliable if you need to do a full recover. And it often forgets to save stuff..