In short yes.
In 1957 you could order one or both tops. All Thunderbirds were built with the ability to use either top. I am sure you have noticed that on the rear deck the plate that is used to lock down the rear of the top uses only one of the two holes on each side. the other set of holes are for the convertible top. I do not know why that is just the design. when you look on the floor behind your seat you should see on each side two studs. those studs are for mounting the swing bar for the convertible top. It is not necessary to use them but without a swing bar the top does not fold up and swing down. Otherwise the top is very heavy to manhandle around. Prices vary. If you want the highest quality I believe Jewell is the source.
good luck , J.
Hi WEL, My 56 came only with a hard top from the factory and I wanted to have a soft top to raise and lower as needed. I ordered a repro top and the swing arm assembly and it came with all attaching hardware. It took only a couple of hours to install and adjust. I purchased it from Hills Thunderbird in Ohio about a year ago. It took about six weeks to get it from the time ordered, but that may have been due to it being a custom color. -Kip