Based on sound, I don't think so. Even if I don't understand the language I can at least be able to tell apart the voices and keep in mind their individual differences. And from that I don't think I'm hearing the exact same VA casts across different shows.
I'm not a VA expert or anything but I noticed that certain new voice actors or actresses get multiple lead roles per season. I recall Kaji Yuuki getting lots protagonist roles in consecutive seasons, like in C3, Guilty Crown, Ro Kyu Bu, and High School DxD. And now this seasons he's in EVOL and Accel World. His voice hasn't really sounded drastically different per role. A handful of other reoccurring VAs along with him in the recent seasons might be giving that kind of impression of casts sounding similar.
Kana Hanazawa is another example and she was appearing in almost half the shows in the previous seasons. She too got lots of lead roles and people might unknowingly notice her voice in different shows. But from I remember, only a few, like 3-4 do appear often in different shows in one season.
If you're determined to show that your friend is wrong, just copy and compile the cast list of all the well-known anime this season or last and show him whether or not the casts are the same.