Luckily, there are ways to know if someone deletes your request. If you do decide to request someone, there’s a chance that they could decline your follow request. If the friend is already following them, you can simply tell them the reason why you want to check the private account and they’ll happily let you view it. If you want to look at someone’s private account without requesting, so you can look at their follows, or posts, you need to get a friend to follow the private account so you can see their followers from their phone. So no, you can follow a private account without requesting.
For them to accept your follow request to view their account, you first have to follow them to request them. With private accounts, the privacy barrier can only be bypassed when the owner of the account accepts your follow request. Unfortunately, there’s no way to follow someone’s Instagram account without requesting them first.