Since it sounds like you are going to be assembling the video using a Video editor of some sort, like Sony Vegas Pro let's say, then the answer is... no...you don't need to pre-upscale the video. Just setup your video project as you would if all the video source files were the same resolution, in other words don't even think about it. Just drop in and edit without thinking about resolution of the source.
When you output the video editing program will create the final video in whatever format you designate, 1080p for example, performing the upscaling on the 720p content as necessary.
Don't waste time or space upscaling the 720p content. First off you are applying an unnecessary compression pass against the source (and the source will ALWAYS be better than reconversions. Secondly the video editing program can do the upscaling from the source format (720p).
In general keep this rule in mind. For the best results when editing don't modify the source. Keep it in it's native format, and resolution, and create your final video in the editing program. Now there are always exceptions, for example if you use a crap editing program, but since I assume you won't be the rule applies