TN Canadian collected US unemployement benefits while in US

[STRIXO 1]

I'm filling for an AOS through marriage from TN to permanent resident while in the US. For the past 5 years I have come to the US as a TN/ temporary worker working for the same employer 6 months out of each year. Each I-94 I was given was good for a year, even though I was only guaranteed work for 6 months per my hiring letter. In 2011 I stayed in the US on furlough - my employer was expecting to have more work for me, but I wasn't working for a period. During the time I was on furlough and still in the US I collected unemployment benefits from the state of California. CA employment department asked me for a valid authorization to work in the state. I presented my TN that was valid until March 2012. They decided I was eligible.

Questions:

Was I allowed to collect unemployment benefits from the state of CA in 2011 while in the US? I'm concerned that USCIS might reject my application on the ground that I shouldn't have collected unemployment from a US state while in the US since technically I wasn't allowed to conduct work search in the US while still in the US. Also, it's one of the Yes or No questions on form I-485.

During the interview, would you recommend I bring a letter from my employer stating that I was indeed on furlough and that he expected to have more work - even though it never happened? Or would it be volunteering information?