Yes it is normal for male birds (at this age and older) to feel hormonal urges and they can/do attempt to mate with pretty much anything, including other species (humans included!). While that act in itself is harmless, it is the associated behaviors that you have to be mindful of.
I can say, from past experience, that Conures and Cockatiels both can exhibit possessive/protective behaviors - which may seem amusing/cute initially but can become undesirable and dangerous if left unmanaged.
If your bird(s) start to exhibit undesired behaviors in protection of their objects of affection, you should make immediate moves to address those.
WallyBirdie - I suggest that you be very careful with allowing your young Conure to interact directly with your budgie. He could become overly attentive and cause injury to her - either accidentally or intentionally.
