Do American English speakers who pronounce cot and caught as [kʰɑt] pronounce all, tall, Paul, etc. with the same vowel quality?
If my subjective experience is anything to go by, I feel like I've heard Americans say [ɑ] (similar or identical to the vowel of palm, with no lip rounding) more in cot, caught, don, dawn, stock, stalk, etc., yet [ɔ~ɒ] (with rounding, similar to AmE north but with no R and to RP thought) more in all, tall, Paul, etc.
If this is true, it can be construed that either
(a) the so-called cot–caught merger is incomplete before tautosyllabic /l/, just like with /ɹ/ (compare thought and north), i.e.
ɔ → ɑ / _ [-liquid]
(If this is true, doll has to be pronounced differently from all because it has /dɒl/ in RP.)
(b) there is a conditioned allophone of /ɑ/ that occurs before tautosyllabic /l/, i.e.
ɑ → ɔ / _ [+lateral]
Note that dictionaries are most likely of no help, because, in phonemic transcription, whether the vowel is transcribed as /ɑ/ or /ɔ/ is a rather arbitrary choice, unless there is a minimal pair of /ɑl/ and /ɔl/ (which there isn't AFAIK).
Am I right in my assumption, or maybe I'm mishearing the velarization of /l/ as rounding or something?