The hiring dept will only contact your current HR to ask for your employment records only if they are 100% sure they want to hire you. Then when they do, your superior will be informed by your HR.

Before the final decision, they will ask you to verbally check with your HR and superior the release date and conditions first. My advice is, you should probably inform your superior sometime between the time you are asked to go for the final interview and after you are verbally offered the job. This is good manners and you won't accumulate bad karma by pissing off your current bosses if you quit on short notice, especially if you are still intending to be in the CS where word does get around about people's reputation...