Congratulations on getting a place in Medicine. Going by first principles:
1) Yes, you should always seek out help and support for your mental health issues. There have been some previous good answers on where you can turn to seek help more discreetly in Singapore:
How do I get help for mental illness in Singapore?
2) You should never hide a record or medical condition that could negatively affect patient care. The repercussions, if you get found out later, could affect your career more adversely.
That being said, the answer to whether it will affect your fitness to practice in Singapore, as determined by the SMC, is that it really depends.
Ie if your depression is well managed because you are seeking treatment, then there should be absolutely no reason why the SMC (who are made up of a bunch of doctors as well) will deem you unfit to practice in Singapore.
If, on the other hand, your depression is poorly managed because you did not seek help and treatment for it, then it follows that they will rightfully act to flag this out to prevent possible harm to yourself and patients.
For now, I'd strongly encourage you to seek out help.
