Rebecca,
Welcome to the site. While you could be of use as a chaplain without leading services, I would highly discourage it. This is a big role for Jewish chaplains and it would be very frustrating for Jewish troops to finally get a rabbi in town, only to discover that we still won’t have someone to lead services.
However, from what I gather from your questions, your bigger hurdle would be the issue of being a rabbi. In order to be a Jewish chaplain, you must be an ordained rabbi. If you come from a non-egalitarian background, then I doubt that this is an option for you.
Another important aspect of being a chaplain is dealing with Jews from all walks of life and all ranges of observance. The vast majority of (but not all) Jews in the service are not Orthodox. It doesn’t mean an Orthodox chaplain has to abandon his or her beliefs, but you need to be open to meeting the needs of those with different practices.
You could certainly be useful as a lay leader, but I would probably advise against pursuing the chaplaincy if you are completely closed to the idea of leading services.
You are correct that being an observant Jew in the military can be lonely at times, but there are plenty out there that do it. You would most definitely be less isolated and have more resources available as a chaplain than in any other occupation.
Best of luck with your decision, and let me know if you have any more questions.