The Rambam (Hil. Korban Pesach 1:5) writes that if one shechts, sprinkles the blood or burns the eimurin of a korban pesach while one of them has chometz or one of the chabura has chometz, all those playing an active role in the korban (שוחט, זורק ומקטיר) are in violation. The implication of the Rambam is that the members of the chabura, even the one who has chometz is not in violation since they are not doing any active part of being מקריב the korban. Tosafos writes that the one who has chometz is not in violation. However, Tosafos gives two explanations why the member of the chabura that has the chometz is not in violation: 1. The Torah says לא תשחט implying one who does an avodah. 2. It is a לאו שאין בו מעשה so there can't be malkus. The Minchas Chinuch (Mitzvah 89) points out that according to the first answer of Tosafos it seems that the בעל החמץ is not in violation of anything, whereas the second answer of Tosafos implies that he is in violation, just that he doesn't receive malkus for a la'av sh'ein bo ma'aseh. Rashi seems to disagree with both the Rambam and Tosafos. Rashi on the mishna writes that if one of them has chometz, they are ALL in violation, implying that not only is the בעל החמץ in violation, but all the passive members of the chabura are also in violation.
Another issue is whether the violation of this לאו invalidates the Korban Pesach. Tosafos writes that the Pesach is kasher since there is no repetition to indicate that the violation of this would cause passul the korban. The Rambam also writes that the korban is kasher [In the pirush hamishna he also writes - ולא יפסיד הזבח]. The kesef mishna points out that this is the implication of the mishna since it only says that you would violate a לא תעשה and doesn't mention the korban.
There is a Mishna L'melech that discusses whether the זורק or מקטיר would be in violation of a korban pesach that has already become passul. Is the violation of לא תשחט על חמץ only on a kasher korban pesach, or even on a passul one? The Mishna L'melech proves from a Yerushalmi that it would not apply to a passul korban pesach. In the Yerushalmi, R. Shmuel says that from the fact that the issur even applies to the zoreik, it must be that the pesach is kasher. Meaning, if the korban pesach that is shechted while one has chometz is passul, the korban would have already become passul by the shechita so that the zoreik would not be in violation. The fact that the zoreik can also be in violation implies that the korban is not invalidated by being shechted with someone having chometz. The entire approach of R. Shmuel in the Yerushalmi assumes that on a passul korban pesach one cannot be in violation of this prohibition.
The Tzlach suggests a similar lomdus to the mishna l'melech in his understanding of Rashi, from which he tries to prove that the korban would be invalidated by being shechted while someone has chometz. Rav Papa says that the מקטיר will also be in violation of this issur. Rashi explains that we are speaking about a circumstance where none of the בני חבורה had chometz so that there was no violation until now, the one who burns the korban on the mizbeiach will be in violation if he has chometz. Why does Rashi need to say that we are speaking where the בני חבורה don't have chometz? It must be that Rashi assumes that if the בני חבורה had chometz so that the issur was already violated by the shechita, the korban would be פסול, therefore the מקטיר would not be in violation. Rashi assumes like the conclusion of the mishna l'melech that on a passul korban, one cannot be in violation and therefore needs to make the case where the korban was not invalidated. The Tzlach later rejects this diyuk, but according to this diyuk, Rashi would hold that the korban becomes invalidate if any of the avoda is done while someone in the chabura or one of the makrivim have chometz.