You’ll have to check with each individual school. It appears that HMC does offer some research opportunity, but the range of available projects/labs is very limited. It is, first and foremost, a teaching-focused school, not a research institution. That means it’s not really set up to handle large MURI-type research programs, and the fairly small faculty size means the breadth of types of projects available will be more limited as well. That’s not to say this is necessarily a bad thing. It’s just one more factor to consider.
Two things: First, payscale is a terrible measure of anything. It’s a self-selected sample of graduates of a school, not a representative sample. Second, salaries at a given school depend largely on major and geography. HMC is primarily a STEM school (which has a higher average salary than other fields) and is located in California, which has a high cost of living (and associated high salary). Does an engineer make a meaningfully larger salary than one from UCLA? Probably not. Do they make more than an average engineer from Purdue? Probably, but likely not when controlling for cost of living.