Absolutely! I don't believe any reputable home inspector will give a home a "clean bill of health" without thoroughly inspecting the basement. Especially when you have pipes and utilities running in there (which most homes do)
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No unfortunately a home inspection usually only covers structural and electrical, you would need a plumbing inspection as well which covers spa's, sewer line, taps, baths and everything else plumbing...
because a house can look like it is in really good codition but have tens of thousands of dollars worth of damage you weren't expecting. mold,termites,electrical,roof,plumbing,heating and air,...
If the company is good one it will be using Infrared Thermal Imaging or Thermography. An infrared inspection can identify several things like electrical problems, missing, damaged, and/or wet...
It is a process wherin a licensed inspector systematically checks almost everything in-and-around a house to determine the current condition. This can include; electrical outlets, switches, fans, A/C...