Hi Robert,
You can select the instance of your system that shall be used as a background sever but please note that if it is different from your central instance then whatever path you have defined while starting SUM tool should be mounted on that application server.
If you want to choose /sapmnt/SID/SUM as a upgrade directory then you can do that by using option:
./STARTUP "upgdir=<path>"
But make sure that this mount point should be available on application server and enough space should be there as upgrade will create lots of logs.
Another thing is when your upgrade will enter the downtime phase all the background jobs are started on your central instance by default and all the other application servers will be shutdown.
So use of application server can be taken only till downtime phase starts.
Regards
Ranpreet Singh