[tunap]

Very possible to import immigrants, illegally or through visas, to labor for below market rates.

[ctlby]

If they're willing to labor for those rates, they are "market" by definition.

[bogomipz]

The OP's question was:

"of the advancements unions have brought to employees in the US over the last 10-20 years?"

Not what's possible. Also local trade unions are not really involved in federal immigration policy.