The other answers have already covered that redirecting would be a bad/pointless response and that simply dropping the response with a suitable status would be preferred. However, you did ask some other questions...
will the other destination be aware of my Server IP?
You used Google in your example. Being a search engine they will probably discover the redirect from crawling your site. So yes, they will know your Server IP.
However, some arbitrary website that you are redirecting to will be stuck with looking at the HTTP Referer on the inbound request (if any) and resolving that to find your server IP.
However, any "illegal attempts" are more likely to be from automated bots which may not send the Referer anyway. After all, this would be an additional, unnecessary step for the bot.
Of course then all these kinda illegal attempts will be redirected to ...
This is assuming that these malicious bots even follow redirects (it is, after all, more work). For something like a "login page" that is a known URL they are specifically targeting, why would they follow a redirect? If they don't get a meaningful response on the initial request then abort. But even if they do follow some redirects, it would be trivial for the bot to ignore some nonsense targets... "Google", "Return to sender", "Disney" etc.
Instead of blocking the incoming attacks, or sending to to somewhere else, you could redirect them back from where they are comming from. Thus perhaps breaking the attackers system ;)
I've seen this "science fiction" idea mentioned a few times - but I can't imagine this working as intended in the real world. It's either going to do nothing - the bot simply does not follow the redirect, or in the case of a serious attack, it's going to compound the problem and flood the network (or someone else's network) with traffic. Either way, the bot doesn't care.