Yes, you can get motorcycle insurance without a motorcycle license, you may be required to have a driver's license however to rate on or be required to get a motorcycle license within a certain period of time. If you can get your motorcycle license or endorsement before applying for insurance for your motorcycle it would be helpful but not necessarily a requirement of an insurance company.
Car insurance and motorcycle insurance providers know that sometimes you have a vehicle to insure before you get your license and thus will start your car insurance or motorcycle insurance policy while you are still unlicensed. Typically when they do this however the will state that to keep the policy in effect you will need to get the proper license within a specific time period, normally within 30 days.
Motorcycle insurance companies know that in some states you must take a motorcycle training course before you can get your motorcycle license or an endorsement for a motorcycle added to your driver's license. For example, in Florida you must take and pass a basic motorcycle rider course before you are eligible to get a motorcycle only license or can have the Motorcycle Endorsement added to a FL driver's license.
If you buy a motorcycle to drive for the Basic Riders Course in Florida then you of course would want insurance on it. I'm sure you'd hate to crash it during the training course and not have Collision on it to pay for the damages. Insurance companies that offer motorcycle insurance understand this and so usually will allow you to start your motorcycle insurance policy without the license since you may need insurance on a bike to take the course to get the license.
When applying for motorcycle insurance an insurance company will ask if you have a motorcycle or endorsement or license however it will really depend upon their internal guidelines if they will allow you to obtain insurance for the bike without having the motorcycle endorsement/license yet. If you have an driver's license for automobiles than the insurer can rate you using that license however it is preferable that you have the motorcycle license or endorsement on your license so that the insurance company knows you will be driving the bike legally.