If you are truly bipolar ANY SSRI (including tricyclics) is extremely unwise and would drive you toward the manic side, it can happen as fast as a few days. If you are concerned about bipolar disorder I recommend that you see a competent psychiatrist to manage your meds. You probably need a mood stabilizer, not an antidepressant, but this may be well beyond the expertise of your GP.
I am not sure I understood the meaning of switching. If you mean to relieve depression then it would eventually. But celexa/cipram is not a strong SSRI so it might take a few weeks not many.
If you mean on the contrary switching to mania then if you are BP2 then for some it does and for some it doesn't especially if they add a mood stabilizer or an atypical antipsychotic like the strong zyprexa say. For me for instance it took 6 months to be manic.
A rule of thumb for bipolars is to avoid antidepressants in general whether SSRI, SSRE, etc... even st John wort When I am low I take vitamin B complex. Perhaps week in your case but it sure helps.
Your 1st sentence is vague to me. You say Been prescribed Celexa but Doc is considering that I might have bipolar 2, is the same doc who has prescribed celexa the one to have concluded BP2 or for instance you were prescribed celexa by a GP then your pdoc told you to stop it as you may have BP2.
Incidentally all pharm companies marketing antidepressants say they don't drive people manic yet they do. There was this SSRE called stablon/coaxil by the French company servier announcing it doesn't give mania as it is a selective seretonin reuptake enhancer so it shouldn't yet it did to me after a year.
There is no way to know that. It would be different for everyone, just as it varies in how long an antidepressant takes to become effective (4 to 6 weeks).