Generally, gas piping should be sized correctly for the appliances that are to be supplied for each branch. The branch lines need to be "large enough" to supply the necessary gas volume without too large of a pressure drop. Having oversized gas lines is not likely to be a problem, but having them undersized would be. Sizing the lines properly requires using published tables from the fuel gas code, or other sources.
The person who installed the "T" probably believed that the reduced size branch would be adequate for the anticipated expansion. Whether it is or not, depends on the size of the branch, total length of piping from the appliance to the gas meter, and other factors such as the supply requirements of the boiler, size of the line prior to the "T", etc.
If the reduced size "T" outlet is 3/4" nominal iron pipe, it is very likely adequate to supply a stove. If it is 1/2" diameter, it may still be adequate. Determining this would require someone who has access to the tables, and knows how to use them.
Please keep in mind that gas is dangerous, and if you are doing the work yourself, you definitely need to do proper testing, including a permit and inspection. Many areas do not permit homeowners to do their own gas work.