Yes when you get a quote or sign up for Insurance through Geico Insurance or any other Insurance company Geico Insurance and other Insurance companies will run a credit check which they base your insurance premiums on.
If your credit is good or pretty good then your insurance rates will be less but if you have a low or bad credit score then you'll pay a higher monthly premium for your insurance rates.
Shopping for insurance though will not harm your credit because although the Insurance companies put an inquiry on your credit report the Inquiry is not a hard inquiry like loans applications put on your credit rating but instead the inquiry is a soft inquiry that does not harm your credit rating or affect your ability to get any loans.