Yes. You can start using Tempdrop straight away, even if you are using another form of birth control, such as hormonal birth control.
Tempdrop is not dependant on your cycle status. However, the sooner you start wearing Tempdrop, the sooner it can get through the 'learning phase' (Tempdrop learns your sleep and environmental patterns). This will enable you to catch your first ovulation post hormonal birth control (HBC) or postpartum (PP), whatever your personal circumstances are.