While there are those here who will state that a scope with an earthed case can under certain circumstances be dangerous, I am firmly of the opinion that all equipment with a metal case should be correctly earthed.
If you need to "float" the scope case, you are using a bad measurement technique.
An unearthed case will probably float at around 120v (in the UK).
The Y capacitors in the mains filter are connected from neutral to case and from live to case, and make a nice potential divider.
When the case is touched, it will feel "tingley", it is unlikely to hurt you, but is could easily kill any semiconductors in the circuit under test.
JimB