Yes.
But safety razors are called safety razors for a reason – you will not inflict life threatening damage.
You will not look like Norman Gunston (try Google if you are too young) and you will not be bleeding all day.
… it will be just a nick and it will stop within a couple of minutes …
When you are starting out with a safety razor you are likely to nick yourself – but it will be just a nick and it will stop within a couple of minutes if you use a styptic pencil and a bit of pressure.
Important job interview or wedding day? Don’t decide to start shaving with a safety razor that morning.
Start on a day when you will not be worried about the result and you can enjoy the process.