I think that what you want to do is possible and many have successfully done it, but you need to be clear on what is involved, and what the implications are. Assuming you are planning on making official aliyah, If you are learning full time, you won’t need to go to the army. But in that case, how will you support yourself? If you are working, you will need to go the army, unless you get an exemption for a health or another reason. Making aliya is a prerequisite for getting a job. No one will hire you otherwise.
The other possibility is to work for an american business (telecommute). Then you don’t need to make formal aliya, and won’t have to go to the army. Additionally, you won’t start losing your aliya rights before you’re ready to exercise them. Ideally, it would be best to make aliya when you’re actually getting married.
Yes, people do get married in Israel, but you will have to be your own advocate to shadchanim since you are on your own and won’t have your parents to help you out with this. Of course a rebbe/good friend/family member in israel can be your advocate too.
The most important thing when coming to Israel on your own is having a support system. Without this, you won’t last long. This can come in many forms.
Good luck!