Actually, when you apply on airlineapps.com it tells you not to include any military conversion for flight times. Although it still makes you put in PIC, which is really what you determine as PIC. I used all my primary, secondary, EP and IP time, plus 90% of other time after upgrading to AC.
They never asked about it at all in the interview. I think they just care whether you have the mins or not. I know one person who interviewed with me who had over +10,000 hours and didn't get hired.
As for connections, I had one with CAL, but I think what really helped was going to an Air Inc job fair. After talking to a CAL HR person at the fair, I got a call within the week.