Do Americans who have the cot–caught merger pronounce 'all', 'tall', 'Paul', etc. with the same vowel quality as 'lot'?

I don't know of any good summary of this, but I do recall heard accounts from specific speakers who say that they use something like [ɔ] before /l/ as a conditioned allophone of /ɑ/.

I would be very surprised if any speaker had a merger that applied in all environments except before /l/. It seems hard to prove that nobody has this, but I'm not familiar with any speaker who says they have this.

One thing that may be relevant is that even in accents that maintain a phonemic distinction between /ɑ/ and /ɔ/, British English /ɒl/ actually often corresponds to American English /ɔl/. I don't know of any good description of the exact contexts that conditioned this, but my impression is that for many non-cot-caught-merged American English speakers, /ɑl/ has a restricted distribution, occuring mainly or only before vowels. Judging from dictionary transcriptions, /ɔl/ is more-or-less standard (depending somewhat on the particular word) for non-cot-caught-merged American English speakers when "ol" is followed by a consonant or the end of a word (or in other words, in situations where the "l" is unambiguously a coda consonant). See my list of examples in What source explains the different pronunciations of "hol" in "alcohol" and "hollow"?

There is also a word spelled with "aul" where British English speakers all have short /ɒ/, but American English speakers may have either /ɔl/ or /ɑl/: cauliflower. Also, many British English speakers have /ɒl/ in words like vault, fault, false, spelled with "aul" or "al" followed by a voiceless consonant, but as far as I know non-cot-caught-merged American English speakers only have /ɔl/ in these words.

To sum up, I think your option (b) is more likely to be correct. It's true that speakers who don't distinguish caught and cot do maintain a distinction between north and start, but I don't think this is really analogous to a hypothetical merger of caught-cot with maintenance of a distinction between caller and collar (Peter Shor's example of a minimal pair). Rather, I would expect the pre-l context to be one of the first places where complete merger occurs, but it is quite likely that the merged vowel in this position will be realized as [ɔ], since even for non-merged speakers there is a tendency to use the phoneme /ɔ/ rather than /ɑ/ before /l/ in some contexts.

Merriam Webster Learner's Dictionary uses /ɑ/ in words like ALL, PAUL/POL, CALLER/COLLAR...

Rounding of /ɑ/ in some cot-caught merged speakers can be due to:

a) dark L-influence, but other vowels are affected too, the STRUT VOWEL for example can sound rounded (in words like culture, pulse, wolf, bull)
b) Californian/Canadian vowel shift, it is not uncommon to hear a rounded stressed vowel in words like MOM, POLITICS, DONNA, DOLPHIN, HONEST and these are all LOT-vowel-words.

Many cot-caught merged people (especially those from the Mountain West states, Vermont and Newfoundland) prefer the unrounded pronunciation of PAUL/POL, CALLER/COLLAR pairs...

/ɑ/ in ALL can be heard even in some cot-caught unmerged people from the South, and of course in Northern Cities (as a result of the NCVS).

ALL in various accents> http://www.lel.ed.ac.uk/research/gsound/Eng/Database/Phonetics/Englishes/ByWord/Word_001_all.htm

Some sound samples> https://www.youtube.com/watch?v=OzyxZgccQSk&list=UUxWp_H6QUHf4Qx3clP_jYQg