Doubt it, unless they have other ways to track you like some spyware installed on your computer phoning home or something, and all you have to do is power cycle the router for a new ip if you have a dynamic IP.
If your directly connected to the new like using a 56k modem or other modems and log on to the net from windows when you just log off/on and you have a new IP.
If your at a free internet wifi place and can't control the logon or router then you can't change your ip, unless of cores you use something like the TOR network or a proxy or VPN.
Depends who your dealing with too, if its just joe noobzor hacker then whatever just change ips and who cares to be 100% safe, if your dealing with one of the 14 eyes meaning one of the big cyber command internet warfare centers then it all most doesn't mater what you do theirs nowhere to hide unless your a total pro/ghost on the net.
Same gos if your dealing with a scary botnet with millions of computers.
I know i got hacked hard once and that scared me.
I know as well in the after math once i was back up and running some weeks later seeing as all my computer died in the first attack i had a botnet on my case or something for a time and would get DDOS like 3~4 times a day for like 12 weeks, don't know how buddy could keep finding me but it turned me in to a tinfoil hat when it comes to privacy & computer security.