I feel this post does not violate my declaration that I will not discuss geirus issues on this blog because Kerisos 9 says because of "ledoroseichem" we have geirus even when there is no Beis Hamikdash. And see Tosfos, Gittin 88b s.v. bemilsa. Bimhera yibaneh beis Hamikdash (Sukkah 41).
In Parshas Bo (12:48) vechi yagur itcha ger b'artzichem v'asah pesach laHashem, himol lo kol zachar.... Rashi brings a Mechilta: maybe anyone who becomes a ger should bring a korban pesach right away, talmud lomar v'haya k'ezrach ha'aretz....
What is the hava amina that a ger should bring a Korban Pesach right away?
Now, gerus requires milah, tevila and korban. See Rambam, Hilchos Isurei Biah 13:1-4. The Rambam says the source of korban for all of Klal Yisrael is at the end of Mishpatim (24:5). However, we can suggest that perhaps the Korban Pesach itself serves as a korban of geirus. Therefore every ger should bring one. The drasha teaches that they bring a different korban, not a korban pesach.
The Meshech Chachma (Bamidbar 9:7) does suggest this, that a Korban Pesach serves as a korban pesach in place of the regular korban of a ger.
And see Harirei Kedem II 57 about this.