No, they will offer you the job before contacting your employer. The job is subject to suitable references so you you don't get the 'satisfactory' reference they can or will withdraw the job offer.
The normal process would be that you would get an offer conditional on references; you would then accept that offer and agree to the references being followed up; and then your employer would/could be contacted, if you've cited them as a reference.
As your prospective employer would want to know how you function in your most recent employment, then IF you put your current employer as a reference, they'll most certainly contact your current employer to check as to your suitability for your new role.
^ However, as most employers take new staff on a trial basis, and any employment is subject to satisfactory references, they'll most likely do this during your trial period.
My previous employer was when i was much younger and i didn't really make a good go of that job. I know my current employer will provide me with a good reference however it is somewhat of a gamble putting their nose out of joint if i do not get the job...
If you are not offered the job, they will probably not take up your references. Even if you are shortlisted for interview, they still may not take up references until an offer is made. That way, they only have to ask for ( probably) 3 references. If there is a short list of 6, they might have to get and check 18 references, if they do all that before the interviews.
So not much need to worry about your present employers getting annoyed at finding out you want to change jobs.
Be aware that unless it's a personal referee then a company reference is unlikely to do more than confirm the dates you worked there. They won't comment on your actual ability or performance.