Can my corporation pay an eligible dividend if it doesn't have enough GRIP?

No, a corporation shouldn't designate a dividend as "eligible" beyond what its available GRIP balance actually supports. Doing so triggers a specific additional corporate-level tax meant to claw back the preferential treatment the dividend received in the shareholder's hands, since that favourable eligible-dividend tax rate is only supposed to apply to income that actually bore the higher general corporate tax rate GRIP is tracking, designating more than that available amount as eligible effectively gives the shareholder a benefit the underlying income never actually earned.

This makes tracking your GRIP balance before, not after, declaring an eligible dividend an important step, since paying it first and checking the math later can mean discovering an excessive designation has already happened, with the resulting corporate tax consequence attaching regardless of intent. Corporations that primarily earn small-business-rate income, and consequently carry little or no GRIP, are particularly at risk of over-designating if dividend decisions are made without checking the balance carefully.

Because this is an area where a straightforward mistake can trigger a real, avoidable corporate tax cost, confirming the current GRIP balance as part of the process of declaring any dividend intended to be eligible is a basic, necessary step rather than an optional check.