There are 20 years between my eldest and youngest siblings. I would say that the eldest and youngest don't have much of a connection, because the eldest had already left home when the youngest was born, so they never actually lived together.
It will probably be similar with a 15 year gap - they'll be at very different life stages with one almost an adult and one a baby. That doesn't mean it's wrong to do it, just worth being aware that they may not be close, depending on their personalities.
Of course you may have a 15 year old who dotes on their younger sibling, loves looking after them/ playing with them etc and they might have a good connection - it's impossible to say, really.
There's 10 years between me and my oldest sibling, and we also don't have a particularly strong bond. I feel closer to my siblings who are closer to my age because we had more in common growing up.
However, I wouldn't say it caused any problems in terms of family dynamics - you just get on with the situation you are in and it's fine.
I wouldn't worry about a newborn being annoying to a 15 year old - they will be fine, as long as they have their own bedroom and personal space, they'll cope.