Yes. It's certainly the case that support for immigration would be hurt if it were perceived as less economically beneficial.
I don't have hard evidence, but my guess is that the mix, the leaning toward economic immigrants, has improved and has helped to maintain support for immigration. How large is that effect? You've suggested a substantial drop. I'm not sure that it would be a substantial drop, just because I think it's hard to see substantial drops in attitudes toward immigration, even in the presence of things such as the Syrian refugee crisis in Germany.