No. The nucleic acid is what contains all the information necessary to replicate the genome and the proteins that encase it. It's the blueprint. Even if what you suggest was to happen, all you would get is a blueprint enclosed in a different envelope to usual, but the blueprint would carry the information for making the original envelope type that blueprint came in in the first place. You can only get something new if the genome changes.
I'm going to stick with the letter analogy here, because I think it works.
Imagine a virus like a scam letter trying to get you into a pyramid scheme. Your friend sent you it. It contains all the instructions for writing letters to recruit ten more friends into the pyramid scheme. The outer shell is the envelope, which the letter also tells you how to fold and seal. You provide the paper and the pen, just as your body provides the raw materials and work to copy the virus. If you get multiple letters at the same time, you follow the instructions from one to write a bunch of copes and send them, and you follow the instructions from the other to write a bunch of copies and send them, each individually. That's your basic virus and how it works.
Now, in the flu example, because that virus, unlike a coronavirus, is segmented, it's like the pyramid scheme letter comes on several pages. You need to put a copy of each page into the envelope, because one explains the get rich quick scam, one explains how to send it to people, one explains how you should phrase it, etc. For the full scam to work it needs a copy of each page inside the envelope. However, if you have two copies of the letter, each from a different source, with a few subtle differences in the spelling and grammar of each page, and drop them on the floor, then you can still assemble a working version of the letter, from the pages available. You just include one of each page, regardless of the source, and send them on their way. The result is a new version of the chain letter, which when someone receives it, they'll copy that version exactly and forward it to their friends as they received it.