Yes, that's true. This て is a particle (接続助詞). The main meaning of this て is "to do something, and then~", that's exactly why the -te form is used to connect clauses.
In 学校文法, which Japanese students learn in Japanese school, the form attached to this て is treated as a conjugation form of a verb(連用形). For example, for the -te form of 取る, 取っ is 連用形 even though it ends with the small "tsu".
In classical Japanese, the -te form of 取る is 取りて, and it changes to 取って because of the geminate consonant euphonic change (促音便). As you can see, 取り is the same as 連用形/the -masu stem of 取る. Thus, 取っ is just a variation of 取り.
Similarly, other forms that are attached to this て are treated as 連用形, too.
e.g.
書く
書きて --> 書いて (i-euphonic change/イ音便)
Both 書き and 書い are 連用形.
飲む
飲みて --> 飲んで (nasal euphonic change/撥音便)
Both 飲み and 飲ん are 連用形. て also changes to で in this case.
Incidentally, the past form is also interpreted as "連用形 + auxiliary verb(助動詞) た(or だ)", not a single conjugation form, in 学校文法. This た is from a classical auxiliary verb たり/たる.
e.g.
言った: 連用形 言っ + た
引いた: 連用形 引い + た
飛んだ: 連用形 飛ん + だ
cf.
言
います
引
きます
飛
びます
This is another example why 学校文法 is necessary to learn classical Japanese, as I wrote in
another thread. On the other hand, the terms like "-te form" or "past form" are more useful for non-native learners of Japanese who usually only learn modern Japanese.