Nope. You would change into a bear, polymorph spells are all or nothing.
Supernatural and extraordinary abilities are both lost, alas. The specific language from the description of polymorph effects in the Core Rulebook is this:
While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form (such as keen senses, scent, and darkvision), as well as any natural attacks and movement types possessed by your original form. You also lose any class features that depend upon form, but those that allow you to add features (such as sorcerers that can grow claws) still function. While most of these should be obvious, the GM is the final arbiter of what abilities depend on form and are lost when a new form is assumed. Your new form might restore a number of these abilities if they are possessed by the new form.
So maybe if the extra arms were considered a class feature? I don't know much about alchemists. Anyway, first pass, as you're hearing, sounds like a no.
So now the question becomes, how, within the rules, can you turn into a six-legged bear. Because...six-legged bear!
Even if you could carry them forward you still wouldn't be a 6-legged bear, you'd be a bear with 2 arms, right?
legally? have phantom limb cast on yourself whilst in bear form?
:)
if it's something you activate you can activate it after you change. If you can't activate it then you lose it.