There is an option to make your TeXnicCenter autocomplete when you start writing align* and then pressing Ctrl+ Space. So maybe it's better than using a mouse click.
First if you go to your folder shown below, you'll find a lot of xml files and some toolbar icon pictures.

These XML files hold the auto-complete keywords by scanning your input. You can include your own stuff in them by editing these files but if you include too many of them it will just get slower and slower since as the number of possibilities increase so is the time to scan for them.
So if you open the file base.xml you'll see lots of stuff that are being tracked while you type. Note that if you feel that math.xml is a better place to put this then you can use that file it doesn't matter. And we just add the align* environment as shown

I've used Notepad++ but that's not important, the important thing is that it's running on that Run as administrator rubbish otherwise it won't allow you to save the modified file.
After saving the file and opening TXC, if we start typing align*, we have

after using the shortcut Ctrl+ Space

For the TikZers you see that TikZ.xml file right? you are welcome :)