It would depend on his background. To become a Templar one had to already be a knight and once you became a one all your property was put into the communal fund.

Now, to define a knight in the high or late medieval era: You had to own the tools of the trade and know how to use them. This includes at least one large horse, armor, sword, a lot of lances (those things break), and all of that cost a small fortune. In fact, the average knight's kit cost more than the average independent farmer's net worth. This did not mean knights were always rich, as many held it as a family trade and each generation maintained and replaced things as needed.

Also note that in this era the ability to read and write was seen as just another technical vocation. Many aristocrats never bothered to learn it.

More important is higher learning in that era was often confined to clerics of all sorts. To the point that some monestaries supported themselves by teaching people how to read.

Another thing to note is even at the height of the Templars only about 5% if their personnel was in the Holy Land at a given time. Part of this was only a minority of them were actual knights and not nurses, messengers, craftsmen, and administrators, spymasters, and so forth. One of the services they provided was if you made a money deposit at one outpost you would get a coded certificate, which could be exchanged at another outpost for the money minus a fee (this was to counter highway robbers).

Overall, it is reasonable to have your character be illiterate as long as it is not incongruous with anything else. For instance, if he's going to be portrayed as a high effective spymaster or if he spent time in a monestary... He definitely should be literate. If he's the younger son of a bankrupt baron who joined the Templars for lack of a better career option, he might just be totally illiterate.

There is a third option where he can read in his home dialect, but struggles with the accent of anyone who isn't local, and doesn't know the trade languages like Latin or Parisian French. Note that Chaucer's English was a creole language of Anglo-Saxon, Norman French, and Latin.