Obviously the company SHOULD be running proper Exchange backups to begin with. Not doing so is simply unprofessional and shows that email isn't that important to them to begin with. They may say it's important...but their actions show differently. OR just as bad...they assume their sysadmin is backing it up properly and they aren't and haven't divulged that to management.
That aside:
I think you have 3 schools of thought here.
OPTION #1 - the "kamikaze approach"
You simply run the sp3 upgrade on the server. I can tell you from dozens of experiences with Exchange service packs that I've yet to have one result in a catastrophic failure.
OPTION #2 - the "fix what's broken first approach"
You postpone your upgrade and get proper backups working on Exchange and the DC first so that you can rollback properly if something goes wrong. Otherwise, you're simply inviting a disaster. And snapshots aren't proper backups. The built in Windows 2008 R2 windows backup utility can properly backup the entire server with Exchange to an external USB drive in a pinch if you want to get lazy about it. (http://www.techrepublic.com/blog/the-enterprise-cloud/back-up-exchange-2010-with-this-windows-server-2008-r2-feature/)
OPTION #3 - your question's approach
Putting aside the fact that it's technically against licensing unless you already own an additional Exchange license...you could bring up another Exchange server. But man what a PITA. You aren't just "syncing" email as a backup, and when you do "move it all back" you'll have to properly decommission the new server, not to mention the frustrations client's Outlook and mobile devices will have if you don't properly setup this new server as a part of your Exchange "organization". You also don't take into account the possibility that adding this server COULD cause a failure to happen on the existing Exchange server, and without proper backups you could be just as bad off.
My advice...you go with Option #2...then run the SP3 installer on the existing server.