Interesting. If you'd care to, how do you think such a war could go? Also, mind explaining the bolded? I think I know what you mean, but making sure.
The full United States of 1846 had the ability to raise and equip an army and to accomplish the conquest of the West and toward Mexico City at the same time, doing so entirely from scratch. The Confederacy, while having that legacy (as the 19th Century army much like the present one was very heavily influenced by the South) has 11/12 states that would have major domestic problems, to say nothing of preserving the institution of slavery which Mexico had ditched before the
1846 war. In that case Mexico would actually be both in the right as defender against the aggressor and able with much less scruples than the North to wield the abolition weapon against the Confederacy.
Too, Mexico was strong enough to give France a great deal of trouble, this at a point when the British and French Empires were matches for the entire unified USA of the time. The Confederacy would have limited manpower, more limited ability to pay for the war, a great deal of people who would not *want* that war either to happen or to be won, and of course the Union potentially getting involved, too.
I think such a war would also run aground against the problem that presuming some Porofiriato analogue the Mexicans will have a much more stable government than the Confederacy would. So the Confederacy would find some pretext, declare war, and find itself quickly running into an enemy who is rather more united to defend itself against an aggressor and with a lot more veterans used to military service.
The initial defeats are followed by outright routs of the extremely inexperienced volunteer units, whose poor discipline and no doubt being incululated in the cult of the offensive (as assuming the CSA wins despite Lee his tactics will become the standard) even when common sense would say otherwise leads it to being given repeated defeats by Mexican troops.
Emboldened by this, the Mexicans start attacks into Texas itself, promising abolition marches with the Mexican Army, thereby placing the CSA's internal problems further into the question. By this point the question becomes what the USA does.
Without a consistent scenario as to the how or the why the CSA wins that would have a major impact on what the alternate USA would see here. Presuming the USA decides to prevent Mexican grabs of what would no doubt be considered
America Irredenta the Confederacy is no more and is defeated by the US-Mexican alliance.