Will it damage? If ya get boogers in the fuel line!! hahaha no seriously I really think thats quite inventive! But having said that, you really shouldn;t need to prime that way. The pull start should be sufficient enough. How many tugs does it take to get the fuel upto the inlet nipple? (anyone familar with woman should know what that is!..haha)

It can take a good couple of tugs. Now when you prime you put your finger over exhaust stinger to make a seal. If you're not doing that, there's your problem I'd say. If you are doing that It may be that there is a leak somewhere in fuel or pressure line.