Do muscles still hold glycogen reserves if there is no carbohydrate input
Most of it isn't but a little bit is.

When your body has very little glucose and a lot of fat(Which can be the case if an overweight or obese person goes on a low carb diet) the ketones and fatty acids and glucose produced by the liver are used almost exclusively to keep the body alive although a little is synthesized into glycogen.

Specifically when you don't eat anything gluconeogenesis alone supplies enough for 1 day. Then the fat metabolism accelerates because gluconeogenesis is not enough. This is when you get into a state of ketosis(this can also happen in bodybuilders since increased muscle = increased fat metabolism). This ketosis causes fast weight loss from not just water like a lot of other diets but also from fat. This fat then eventually depletes and it metabolizes protein exclusively(during all this time it does metabolise some protein). However that can't continue forever even if the amino acids get reused over and over again because some are used to produce ATP. Thus you eventually would die from starvation with obese people surviving longer than underweight people.

Anyway as far as exercise assuming that you start off obese, getting your body into a state of ketosis makes your performance even better than on just glucose alone after a while of adjusting to fat metabolism since 1 molecule of palmatic acid(16 carbon fatty acid) produces 106 ATP compared to 32 ATP for 1 glucose molecule so your muscles can go longer without being exhausted. Theoretically someone who is 50 pounds overweight could exercise 24/7 for several days if he/she is in a state of ketosis.

Here is a reference to the low glycogen and increased muscle performance:
http://www.bodybuilding.com/fun/glen12.htm

As to why it is 106 ATP it is because each NADH produces 2.5 ATP and each FADH2 produces 1.5 ATP and because of the activation step using 2 ATP just like how NADH transport from cytoplasm to mitochondria takes 2 ATP, 1 per NADH in glycolysis.