Does Tri-sprintec Start Taking Effect Straightaway On Consumption?

I have been taking tri sprintec birth control pills for two years and have not had any problems. During that time I have always used condoms too. I am now in a healthy long term relationship and want to stop using condoms because I know that we both do not have STDs or HIV. My question is in regards to the effectiveness of the pill when starting a new pack after taking a week of inactive pills for my period. Does it start working right away?