I agree that there's a definite connection, but while Shartan may have been a literal incarnation of Solas, details in WoT2 suggest that Mythal's relationship with Andraste was more subtle: very different from the 'fusion' of minds we encounter with Flemeth.
Mythal's particular domain within the Pantheon is water- a metaphor for the Fade. This matches her parallel in evolutionary psychology, as her domain is the midbrain: realm of emotion and memory, a fitting match for the Lady of Regrets. In the human brain, the major structure related to both is the temporal lobe, which contains the hippocampus (long term memory) and associates emotions with memory.
The interesting point here is how Andraste has been set up to mirror Joan of Arc, given that modern theory suggests her religious fervor was due to Geschwind syndrome, which is caused by temporal lobe epilepsy. The severity of seizures experienced by TME sufferers varies. Some people never even realize they have it, since their only symptom is the occasional odd sensation, aura, or passing sense of deja-vu. Others have slightly stronger attacks that temporarily interfere with their ability to react to the external world, and this is where ToM2's account of Andraste's experience begins to clue us in:
"As a young woman, she would become still for long moments, unable to be moved or roused. After, she would report voices, as though from a lost memory, and talk of strange auras or the sounds of bells."
...which is a textbook description of a complex partial seizure of the temporal lobe. But again, this is Thedas, where the figurative is often transformed to the literal. As we've established earlier, the temporal lobe is Mythal's domain. Could these seizures be in some way the voice of Mythal, speaking to her?
We can't be certain, but I believe so. From all appearances, Andraste was influenced heavily, but never 'merged' with Mythal in the way we usually expect.