Now that is off the table as Russia has formally included large part of Ukrainian coast into Russian Federation.
Indeed there is an example of Belarus, which is a smaller country that is still independent (in the sense that it has its own statehood, laws and international relations) and intact. If that is what you mean by independence, then if Belarus pulls it, Ukraine could also.
If by independence you mean the ability to persistently ignore your largest, trigger happy neighbour concerns - indeed such independence was likely doomed from the start. That's the "flashing jewelry" part for you.
And again, I'm not really talking about personal choices (maybe Ukraine did have to go through Second Independence War like USA did), but about the desirability of such scenario to be copied by other countries.