You're assuming the version of electrum you downloaded from the software center is the same as you would have compiled yourself. Why risk it? Just download the tools to compile your own copy.
If you're going to assume any one piece of software in the official Ubuntu repositories (which the Software Center installs from) is compromised, you have to assume they could all be compromised. In that case, you also have to assume that your installation disc (built from those same packages, by the same people who maintain those packages) is compromised. Better ditch Ubuntu altogether and go with Gentoo or Linux From Scratch in that case.
Realistically, though, Electrum is a Python app. It might be compiled to an EXE on Windows, but on any other operating system the source code is what you run and there's no real need to compile it. Technically the Python interpreter will compile it to an intermediate byte code (.pyc files) but that's just an optimization and the .py (source) files will be used if they don't match the .pyc files.
Out of the box, Ubuntu does contain some things that some of us might consider to be adware or spyware, but it's not hard to remove those things (which don't matter on an offline machine anyway). What is there is far from being the kind of wallet stealing trojan you'd be worried about, it's mostly there as a way for Canonical to make some extra money off of the mostly free distribution of their Ubuntu Linux OS.
BTW if you're so worried about Ubuntu that you want to compile your Linux OS from scratch, keep an eye on Gentoo as well, some packages contain some pretty controversial patches and if you let Portage install them those patches will be installed along with them.. so compiling everything from source isn't necessarily the silver bullet you make it out to be either.
