When it comes to this aspect, any relevant background will give you an edge. Some experience is a big plus already since construction estimators in different companies do not have the same trainings particularly that each company has its own specific estimating process. When you are hired by a new company then, you will be expected to be trained according to their set of standards as well as learn new things that your previous company doesn't have.
Working as construction estimator will open up many ideas and knowledge as you are not only interacting with one kind of construction people but almost all of them. So, an experience where interacting with various kinds of people was the main component of your job can be a great advantage to you when applying for this job.
Development opportunities for you
The advantage of becoming a construction estimator is that you can take this as a path towards a higher career with higher paying potentials in a construction jobs field. Once you have become a construction estimator, you will have the opportunity to select specialized field in this area. For example, if you are done with the general estimating job, you can opt to specialize in mechanical or electrical estimating.
There are appropriate trainings for this, so you might be required to have them before you can move on to another level. However, if you plan to be in your existing position, you can have the opportunity to work on a senior position giving you the benefits of higher pays, higher employee value, and interactions with more prestigious construction projects.