Absolutely, the entire system would be even more overwhelmed than it is already.
I don't know which dummy originally came up with the idea of "import immigrants to pay for the healthcare of the boomers" but whomever it was undoubtedly loathed his parents.
As it turns out, immigrants have parents, love them and that being able to help them when their health is failing is incredibly important to them.
Immigration is no solution to the problem of having a low birth rate.