Compost is a gardeners best friend but it is not the ideal choice for seed starting. Short answer: yes you can. The better idea is to use the compost in the container or garden after the plants are firmly established and growing. (and can really use the nutrients)
Compost is nutrient dense and just not necessary for seed starting. My suggestion is to use it where your plants will benifit the most from Gardeners Gold, the compost.
A light, airy seed starting mix is ideal for seed starting. You can even make your own seed starting mix by combining coconut fiber or peat moss with equal amounts of the compost and a hand full of vermiculite.
This will help you stretch your valuable compost.