Actually, you will be able to feel undestructible in PvE if you have a battleship/dreadnought/whatever. Suddenly, many missions can become a cakewalk, if you like doing them. But that's it, I think. PvP is a completely different territory.
I can still remember when I was flying around here in my beginning week, and when I came up on my 1st battleship, I thought it was the coolest thing ever & decided I'ma get me one.
Having learned alot since then, you might think I'd attempt to discourage you from going that route & advise you not to get one...honestly though, I advise to get one if you really want one.
If you hate it, then it's better to regret something you have done than something you haven't...but unless you try it on for yourself, there ain't no amount of outside wisdom that can truly speak to you.
There are people out there that love flying those things & for all you know, you just might be one of 'em.