If they attempt to annex Iranian Azerbaijan (a territory arguably even larger than the Republic of Azerbaijan itself), it will likely backfire against them, assuming that the coalition/the US/Russia even permits them to do so to begin with, the first problem is that what "Iranian Azerbaijan" means is up for debate, since Azeris live way beyond what is traditionally considered the "Iranian Azerbaijan", and there are plenty of non-Azeri minorities inhabiting it, like the Kurds, Talysh, Gilaks, Tats, Lurs, and the Persians themselves, and Azerbaijan is a country where non-Azeri ethnic minorities are subject to forceful assimilation.
Iranian Azeris and Azeris in Azerbaijan live in two very different societies, despite both places being majority-Shia Muslim, Azerbaijan's government and society itself is quite anti-religious, it bans Hijabs in schools, prohibits Islamic symbols in public (even in Mosques I think), prohibits foreign Muslim preachers, bans Azeri citizens from getting Muslim education abroad, restricts Azeri pilgrims of going to Hajj, the population is not devoutly religious and sees Islam as more of a patriotic/cultural symbol rather than a genuine faith, and more stuff of that type, Azerbaijan upholds Soviet-esque anti-religious policies that are the extreme opposite of the Shia Theocracy that Iran is.
This weird trend of a Muslim-majority country whose autocratic government severely restricts Islam reminds me of Turkmenistan and Tajikistan, you ironically have more freedom to be a Muslim in the West rather than in these places, hell,
Tajikistan prohibits men from growing beards and wearing Islamic clothing (Turkmenistan does it too), viewing it as foreign subversion, with even incidents of police officers forcibly shaving beards from Muslim men, they also prohibit any foreign bearded men from entering the country! (well, now Tajikistan and Turkmenistan are countries that I'll never be able to visit, and I'm not even Muslim)
Despite the contrast between the two states, there does exists some brotherly sentiment among Iranian Azeris and Azeris from Azerbaijan, but I am not sure if the Iranian Azeris would be happy with out of the blue being completely annexed by the former Soviet republic of Azerbaijan, I also recall reading that Azeris are some of the most pro-Ayatollah non-Persian minorities in Iran, Khamenei's father was an Azeri for example.
Also IOTL, the West has
usually avoided partitioning countries that they intervene in, the Bosniaks, Serbs, and Croats were forced to remain united under a single state even after a bloody war and genocide, and the US also did not permit the independence of Iraqi Kurdistan, despite Kurds being subjected to similar atrocities by Saddam and having a strong wish for independence and separate identity from Iraqi Arabs.
Note: Someone please correct me if I got anything wrong in this wall of text, I read most stuff about this a long while ago.