Short answer is yes.
For this question I shall be discussing what it’s like for any heterosexual person who has a close friend of the opposite sex, as it’s the situation I’ve experienced the most. Unfortunately it doesn’t matter whether consciously you find the other person attractive or not, after getting to know someone and all their deepest, darkest secrets feelings tend to appear. Sometimes without you realising.
An example is when boys don’t like their girlfriends having close male friends. You can still think romantic feelings about someone without being physically attracted to them. You can still enjoy spending an entire day with someone without thinking about having sex with them at the end of the day. And that’s friendships in a nutshell; enjoying company of another person and not needing the intimacy.
However, it’s not necessarily the amount of time you spend with them that makes you gain feelings. It could be as simple as talking to them every day for a period of time. You are able to talk about anything and everything. When you’re down they are there for you, telling you it’s going to be ok. Maybe you mistake that care for something more? Or maybe it becomes something more eventually?
Everyone always says “Dating your best friend in the best thing in the world”. Of course, why wouldn’t it be? If you’re dating the one person who knows you better than you know yourself; that’s a bond nothing can beat. Although everyone has a boyfriend/girlfriend and then their best friend.
Sometimes if you’ve had an argument with your significant other than you go and vent to your best friend. Which is fine, everyone does it. But when that best friend is of the opposite sex, it can cause problems.
Another thing you have to think about is physical attraction towards another person can change over time. In some cases as you get to know someone better you become more physically attracted to them. You can date someone due to their looks and then have their personality grow on you but it can happen the other way as well. You can date someone due to their personality and have their looks grow on you too.
All in all you might not find your best friend attractive but if you connect and can have a lengthy conversation with them; you have a chance of falling in love with them.