Present perfect - indefinite time

The perfect has four general interpretations (CaGEL p143):

the continuative

She has lived in Berlin ever since she married.

the experiential (or ‘existential’) perfect

My sister has been up Mont Blanc.

the resultative perfect

He has closed the door.

the perfect of recent past

I've discovered how to solve the problem.

The continuative is rather clearly separated, but the other three largely rely on context for the correct interpretation - whether the situation in question is recent or not. All three have current relevance in that they are important now, but for different reasons.

The interpretation you're going for is the experiential perfect, which does not imply that the situation occurred within the recent past. It would be the salient interpretation in contexts like:

I've broken my leg, but never my arm.

In sum, you can use the perfect in this way, just make sure the context is right.