You are allowed to run a paid campaign in tandem with your grants campaign. What I recommend to my clients is to use the paid account to run display ads and us the grant account to run search campaigns.
Display can be very effective for nonprofits to create awareness and branding.
Keep in mind that the two accounts are completely separate and that you will be billed for any traffic generated in the paid account. Your Google grant ONLY provides free advertising under the approved grant account.