The DOMS kind of pain is indicative of having exposed your body to something it isn't used to. It's a sign of hard work, but an even more reliable sign is that you did hard work. You know if you've pushed yourself hard or not. You can do very hard work and not get DOMS. You can do light work and get DOMS just because you're doing something different. In short, DOMS is a sign that something's happened, but it's an insignificant sign. Physical pain is not required for any fitness goal.
There are plenty of other kinds of pain than DOMS. You really don't want these other kinds of pain. The only one that's sort of okay to get is lactic acid accumulation pain, which is the "feel the burn" kind of pain, but it, too, is insignicant unless you're specifcally training to adapt your lactic threshold, and your technique on each exercise is likely to give out before lactic acid pain can kick in (at least as a beginner), so it's not something to strive for at this stage. All other pains I can think of are signs of something wrong - a nerve impingement, muscles not firing properly and the body being loaded wrong, muscles being overloaded to the point of tearing, etc.
So, pain is either unimportant, or it's a bad sign.
Either way, whether you feel pain or not is especially irrelevant with regards to weight loss. Weight is lost by your body being in a calorie deficit, not by how much you suffer. Hostages in POW camps lose lots of weight, and it sure as hell ain't cus they get epic DOMS. Not to imply that you should lead a POW lifestyle, btw.