I very much doubt it. While new versions are (supposedly) backward compatible the reverse does not hold true. For best results you should edit with the same version that created the file. Note that you can install multiple versions on the same computer as they are self contained installations.
Insanity is hereditary, you get it from your children
I absolutely agree with Neale.
In fact, I wouldn't even recommend opening an older version project in a newer version of the program! Because the program goes through such a major overhaul each generation, opening any other version's project almost always leads to problems.
Welcome to the forum.
The likelihood that a PrE 8 Project would Open in PrE 7 are very slim. Historically (PrE and PrPro), this has almost never worked. There are usually enough changes, as the programs go up in version, to keep earlier versions from working with the files. In most cases, one can safely go the other way, and the newer versions will convert the older PREL (or PRPROJ in PrPro) to the newer version, though not always.
As has been said, finishing in the version, in which it was started, is always the best.
If one had to migrate the Project, the next best course of action would be to do most of the work in the later version, planning on what would need to be done in the earlier version to finish the Project, and then Export an intermediate file from the newer version and Import that into the earlier version to finish the editing.
For the creation of intermediate files, I like the Lagarith Lossless CODEC, but others might have different ideas.
When following the latter workflow, planning should go into it, as the intermediate file will not have the "loose" media, and everything will be packaged into the intermediate file. You will loose aspects, like Handles, so plan, plan, plan.