I know a bit about this because I have a degree and quite a bit of experience in residential architecture. Here are a couple of my thoughts:
An advantage is only an advantage if it is properly marketed. The trick for you will be to find the balance between selling your construction experience without overshadowing your real estate license, and at first this will be difficult.
Remember that real estate agents are hired to do real estate work and as such you need to honestly state your experience in this realm. For the most part you will be right in there with the rest of the new agents at first. Your construction experience will only be an ansilary benefit at best since they are hiring you as a real estate agent.
Focus more on clients where both of your skillsets will dovetail - rehabbers who need a contractor to do some work. First time homebuyers looking to buy a place and fix it up some (you will help them determine costs, etc.) Vacant land purchasers who are planning to build a house. You get the idea.
Good luck in your new career and post back often with questions you will get plenty of help here. In the mean time find a broker that is willing to train you (they will all hard sell this - the trick is figuring out who is selling and who is just telling you the way it is)
I believe you will have a big advantage! I have been in the real estate and construction business since 1984. I always maintained my license even when I was working as a project manager or as a licensed building inspector. It also opened more doors on the construction side having a real estate license.
I feel I have an advantage with my knowledge when I look at homes for a potential listing or with buyers. Of course you have to be very careful that you don't make yourself out to be an expert as it could lead to legal problems.
I even obtained my certification in real estate as "Residential Construction Certified" and "Certified New Home Specialist".
I wish you the best!