Yes, missed after-hours calls can hurt your plumbing LSA performance badly. Google tracks your answer rate 24/7, and if your profile says you're open for emergency plumbing but you don't pick up at 10 PM, your ranking drops below the top 3 Google Screened spots and your cost per lead goes up.
You often still get charged for those missed calls even if the customer hangs up, so you're paying for jobs you never had a chance to book. For plumbing this is critical because almost half of your high-value emergency jobs like burst pipes or no hot water come in after 5 PM and on weekends.
If you cannot answer live, you are sending a $3,500 water heater job straight to your competitor. The fix is simple, either use a live answering service, forward calls to your on-call tech, or don't claim 24/7 hours in LSA and pause ads from 11 PM to 6 AM.