Not so, I'm afraid, Andiamo.
Soon after you've been approved for an EP, you'll receive an in-principle approved letter. You'll need this document to do your medical test (HIV blood test or X-ray or both).
The in-principle states that it can be used as proof of an EP while the EP is being processed. However, it requires a valid visa in your passport to be validated against. A tourist visa is fine.
Now, if you let your tourist visa expire, thinking that you have your in-principle to fall back on, you're wrong and in violation of Singapore'd #1 immigration rule, which is to never ever overstay. If there's one thing that really pees off the authorities here, it's overstayers, even technical overstayers like in this case.
In other words, always, always do a visa run when your EP is not yet ready, because the in-principle on its own is worthless as a visa.