In principle, yes, but only if you've actually got the appropriate keyboard layout available. It's been a long time since I've used System 7.anything but from memory, you need to launch Apple menu->Control Panels->Keyboard (or Key Layout - I forget) and see what layouts are available.
My not entirely trustworthy memory tells me that System 7.0 is unreliable and you shouldn't use anything less than System 7.0.1 with the tuneup v1.1.1, which I suspect is hard to find these days (Apple no longer hosts these files itself).
This web page confirms the benefit of System 7 Tune-Up 1.1.1:
http://apple.wikia.com/wiki/System_7_Tune-Up_1.1.1
You might consider installing System 7.5.3 or 7.5.5 on your Classic both of which are very much like System 7.0. Go here and look for the link to Tripod in the System 7 section to get System 7.5.3:
http://lowendmac.com/2013/classic-mac-os-downloads-and-updates/
That page also links to the System 7.5.5 update (which will update 7.5.3 to 7.5.5) in the Classic Mac OS Updates section. Some of the links on that page are broken, but I've checked the links I mention.
Good luck.
I've read your comment. I have a second suggestion.
If you've got a copy of ResEdit, you could try the following:
1) install 7.5.3 and look to see if it's got a suitable keyboard layout available via the Keyboard control panel. 2) if so, examine the Keyboard control panel with ResEdit and see if you can identify the appropriate keyboard layout resource. 3) if you can, use ResEdit to copy that resource from the System 7.5.3 Keyboard control panel to a copy (!) of the System 7.0 Keyboard control panel.
It'd be a lot of effort with no guarantees, but just so long as you work on a copy of your original Keyboard control panel and keep a backup of your Classic, you can't break anything.
It's possible that the System 7.5.3 Keyboard control panel might work directly with System 7.0, but then again it might cause problems.