3 answers
Yes, I think so.
Global Search does not search PriceBook Entries, but does search Products. The challenge is that you want them to find a PriceBook Entry, not the underlying Product.
Since all Products have to be a PriceBook in order to be used in an Opp, what is the purpose of someone doing a Global Search on the Product Name? They would still need to figure out which PriceBook to choose for the Opportunity.