My new plant has many buds. Should they be removed when planting and will they continue to make blooms the first year?

If you water them well, it is my experience that they will hold on to most of the buds.

Will those buds flower yet this season if left on the new transplanted rhodo?

I do not know the weather in NE to speak on that with 100% confidence. I just know that I have purchased about a dozen various Rhoddies in my life including three for my son here in MI 5 years ago.
I make sure that those plants are kept watered. I water upon transplant, every other day for two weeks, twice a week for a month then weekly after that until cold weather arrives.
If the new rhododendron is not getting enough water, that leads to stress. Not only replanting stress but newer tissues like new buds and leaves might get sloughed off as the plant can't take up enough water to keep them healthy and viable.
So much of it comes down to water, how much? How often? Well you want the root mass to be moist from top to bottom. If it doesn't get that it is easily assumed that you will experience some degree of die back.
THANK YOU FOR THE ACORN!!!

Also, if you transplant and then warm weather arrives, that can cause rapid drying.

Inside, the buds have already decided if they will produce flowers or leaves. Yes, they will continue to grow. Transplanting rhododendrons is stressful, especially in dry Nebraska, and flowers steal a lot of energy that would otherwise be used by the plant to support health. If the rhododendron is struggling, it will still put most if its energy into the flowers at the expense of its own health, and the flowers will be small, short-lived and maybe even deformed.

So when you can determine if the buds are (or are not) flower buds, you might want to leave a few flowering to see how they look, but if it were me, I would remove most of them this year. Do not remove leaf buds. Leaf buds will also grow immediately under the flower buds, so if you remove the flower buds, cut just above the top leaf (or as close to it as possible), or grab the bud see if it easily twists off.