Teaching ESL with California Credential

I'm currently pursuing my Adult Teaching Credential in ESL through the State of California. The information on their website http://www.ctc.ca.gov/credentials/leaflets/cl697a.html explains that this is one of the requirements to teach in many California school districts (right now I am not interested in working abroad).
Recently I have noticed many classified advertisements from local language schools for ESL teachers who posess TESOL, CELTA, or TEFL certificates. Here's my question ...
If I have a California Designated Adult Teaching Credential with the qualification to teach ESL would private language schools in the USA typically consider me ... OR ... would they recommend that I present one of the above-mentioned certificates?
Thanks for any advice/insight you can offer! :-)

In the US, they should recognise a state qualification.

I agree with Tdol. Many language schools ask for brand-name certificates by default. You should be (more than!) fine with a state-issued credential.

Thank you both!