I am an extremely recent case study...
October 4th: Nearing 45 years old and 186 lbs. at 5'6". According to the intergoogles I was solidly in the lower ranges of obese, considered pre-diabetic and at high risk for heart disease. I like to ski, hike, mountain bike and golf but I would wear down fast in all of those activities. Walking nine holes would leave a mark and walking 18 resulted in me limping in out of breath, muscle tired and usually about +8 over the last three holes.
After years of waffling I final decided to do something about it.
January 1st: Lost ~40 lbs. through diet/nutrition alone. I had reached my goal of mid-140s but now I had just gone from overweight and unfit to skinny and unfit.
January 11th: Signed up with a personal trainer (if you have the means, I highly recommend picking one up.) As I went through my initial evaluation it was clear my strength was sorely lacking Arms, chest, shoulders and back were all weak at anywhere from 25th to 40th percentile. Legs were surprisingly strong (.85) probably from lugging my honorably earned beer belly around ski resorts, golf courses, mountain trails and up the stairs to my second floor bedroom. Cardio was a joke. Started working out to fix all that. And hard. Six days a week minimum with resistance and cardio. Nutrition closely analyzed and good habits established (that was easy after what I did to lose the weight.)
February 26th-28th: Three days at Bandon. If any of you were there last Friday you know how wet it was. As I finished that round I'm sure I was carrying around 10/15/20/whoknows extra lbs. of water. The shoes, socks, hat, bag, head covers and across my shoulders were all soaked through. But... no problems with endurance and strength. Two more days at the resort in beautiful weather and still feeling fantastic. That was a massive, massive change for me. Had a little IT band flareup and my shins kinda hurt in the mornings but both of those quickly went away. Night and day.
Regarding distance, it's hard for me to compare sea level with home at 4300 ft. but if nothing else I do feel that my swing is much better. I'm not having to swing around a heavy body and my flexibility is improved. It feels right and I think this year will be a big improvement. Anecdotal evidence had me closer in drive distance to people I've golfed with previously so we'll see. I haven't golfed enough around here recently to really say but without a doubt my skiing has become much more enjoyable. I can hit it hard from 9:00-4:00 with a 30 minute lunch - no bother. Last year I'd be looking for coffee in the lodge by about 2:00. I am really looking forward to a markedly improved year in golf, hiking and biking endurance/strength.
Some may be talented enough to be good overweight and unfit and golf is enjoyable even when you are. But I think it's a certainty it gets better when you lose that weight and increase that fitness.
I believe that working out improves your game. I know it improves your life.