The Shulchan Aruch in Siman 60 rules that all Misvot require the basic Kavana (intent) to perform the act for the sake of fulfilling Hashem’s Misva. In Hilchot Sisit (8:8), Maran emphasizes that one should have an additional Kavanah when putting on Sisit: He is doing so to remember all of Hashem’s Misvot. This is necessary because the Torah explicitly states that this is the purpose of wearing Sisit. It would defeat the purpose of the Misva if one would wear Sisit without remembering its purpose. The question is whether this extra Kavana is M’akev (Critical) to fulfilling the Misva. The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) cites the Vilna Gaon that this Kavanah is only Lechatehila (ideal) to fulfil the Misva in the perfect fashion. However, if a person did not do so, he has still fulfilled his obligation, B’dieved (after the fact).
However, The Be’ur Halacha (Siman 60) rules that if one did not even have the basic Kavana to wear Sisit for the sake of the Misva, he does not fulfil the Misva, and it is considered as if the garment has no strings. In general, it is assumed that anyone who dons Sisit is doing so for the purpose of a Misva. Why else would one chose to wear a Tallit? However, it is conceivable that if someone put on an undershirt with Sisit attached, like "Neatzit," his intent was for the garment and not for the Misva. In such a case, one must be sure to consciously have Kavana that he is wearing the garment for the sake of fulfilling Hashem’s Misva.
When donning Sisit, it is preferable to have Kavana to not only fulfil the Misva, but that he is doing the Misva in order to remember all of Hashem’s Misvot.