Will insulating pipes shorten the time it takes for hot water to reach the faucet?
Insulating water pipes reduces the speed that they lose their temperature with the ambient air. This can reduce the risk of the pipes freezing in an outdoor location. For the indoors, it keeps the pipes warmer for longer, which may help for frequent tasks that don't require hot water, like hand washing.

But once the pipes have cooled off it doesn't increase the speed that water takes to travel from the hot water heater to your fixtures. If you need to reduce that time, you may want to consider adding a hot water recirculating pump that ensures the water is always hot at your fixture.