Internet connection doesn't matter. All you need is a current firmware version installed before trying to install the US Super Paper Mario firmware version on a PAL/JAP Wii.
I guess it's time to spell it out again...
As niklasnyfiken has said above you want a current firmware version on your PAL Wii, however "current" isn't exactly what's needed to avoid the SPM update bricking.
You require the 2.1E or 2.2E firmware (current version) installed on your PAL Wii to avoid any problems with the SPM update.
By connecting your Wii to the net and updating it you should (at the moment) get the 2.2E firmware which is good. You can also get the 2.1E firmware update from a PAL game disc that has the update on it (SSX Blur I believe) that will solve the problem.
It is possible that future Firmware updates could create troubles for other region games so having the 'current version firmware' is not a guarantee for the future. E.G 2.5E firmware on your PAL Wii may give you a bricked Wii when you play Mario Galaxy on it.. pure speculation but it's a possibility.
The best way to avoid problems (other than sticking to your region's titles) is to read the boards here at GBAtemp to see if their are known problems and/or solutions with particular out of region titles.
You know someone out there can't wait to try it and if possible will stuff it up, this means if you're patient you can avoid their mistake.
To answer the original question though, bricking is possible whether connected to the net or not.