1. I don't hang out with plumbers or electricians, I agree. That doesn't mean I know nothing. There is a substantial literature on this. Now, I would probably know more with data AND personal experience, and I don't have the latter for the most part (though my son-in-law is a budding auto mechanic). I contest the "blind" allegation, which I think is an unfair overstatement.
2. Google confirms my intuition that there are few illegal workers in skilled trades like electrical/HVAC, etc. In these fields, there are way more shortages/openings than illegal workers. Wages are set at the margin, so if the # of openings vastly exceeds the undocumented labor force, then the undocumented workers are doing nothing to suppress wages.
As we reported earlier, immigrants make one in four construction workers. The share is significantly higher (31%) among construction tradesmen. In some states, reliance on foreign-born labor is particularly evident, with immigrants comprising 40% of the construction workforce in California and...
eyeonhousing.org
3. I can't speak to boilermakers or pipefitters. As I said before, construction is one area where undocumented workers are in competition with natives. That does not necessarily mean that wages are being lowered. Remember: undocumented workers consume even as they produce. There are studies suggesting that undocumented workers increase wages because of the increased demand. I haven't evaluated those studies and I find them implausible at first glance, but they were written by serious people. In any event, I'm not aware of any actual evidence that illegal immigration has a meaningful effect on wages. except perhaps in the lowest skill work in construction.