Everything you analyze in roman numeral analysis needs to reflect the key you are in and where the chord comes from. If the chord is not in the key, it needs to be marked appropriately. There is no scenario where you would mark a C7 as vi7 in the key of E major because:
- The standard vi chord in E major is C#, thus a root of C needs to be denoted with a flat to show it is does not have a root of C#.
- The chord is major in nature, so in most styles of analysis the Roman Numerals would have to be capitalized.
So if the C7 was considered a borrowed chord was functioning in E major it would be shown as bVI7, which is very unlikely because of the dominant nature of the C7.
The most likely scenario is you are modulating to either F major or F minor. In either case the chord would be seen as a V7 in each key. Most likely it would not be a secondary dominant because F is not in the key naturally. If it was however, it would be analysed as V7/bII.
There are a few more possibilities that are a little more involved. The chord itself could be part of a sequence where there is some kind of pattern being repeted over, and over agian to take you from one idea to another. Most likely in this case you would analyze it as a modulation. It could also just be a passing chord in which case, you don't analyse it because it is not functioning as a typical chord in the key.