I dunno if 's normal, but it has happened to me. If they're really your friend, back the hell off! Usually, when it happens to me, it's just a little infatuation thing. Not true love or anything like that.
to give you a different perspective: i was always the friend with unrequited feelings back in my single days. it honestly didn't bother me that much when my friends dated my crushes (even serious, multi year ones). i always figured obviously my crush was nothing more than crushing, so someone should be happy. this way two people i care about are happy and i'm no worse off. usually my crush faded as soon as i knew what the person was like in a relationship.
i think it depends on the friendship and your friend's personality. some people can handle rejection (which is basically what this is). some can't. only you will know how your friend will react.