Does large text datatypes reserves storage on disk?
Mot eactly, see mysql manual

TEXT and BLOB columns are implemented differently in NDB; each row in a TEXT column is made up of two separate parts. One of these is of fixed size (256 bytes), and is actually stored in the original table. The other consists of any data in excess of 256 bytes, which is stored in a hidden table. The rows in this second table are always 2000 bytes long. This means that the size of a TEXT column is 256 if size &lt;= 256 (where size represents the size of the row); otherwise, the size is 256 + size + (2000 × (size − 256) % 2000).

As you can see it save 256 Bytes if you have equal or less than 256 bytes.
And if you have more than 256 bytes mysql reserved 200 Bytes blocks till it can store all data