Is Pregnancy Possible During Perimenopause?

I'm 45 years old (soon to be 46) and have been told by my obgyn I'm in perimenapause. I tried to conceive when I was 33 but was told by the reproductive clinic doctors I couldn't due to "atresia?" Sluffing of my eggs at a high rate; those remaining were poor quality. In any case, I had a period on 3.1.11 (25 days since last one) and 3.23.11 (22 days since last one) and 4.17.11 (25 days since last one). I was intimate with someone on 5.9.11 without contraception and it's 5.24.11 (37 days since last cycle). I haven't started my cycle yet. Could I be pregnant?