Yes, you can do this. There are 4 "original" fields you can look for.
Original Search Phrase is the one you need. Assuming that the lead is not logged into SSL google, then the phrase will appear here.
You can then setup a score flow like so:
SmartList:
Original Search Phrase CONTAINS/IS/STARTS WITH "your company" (or other keywords)
Flow:
Change Score "Lead Score" IS +5