Yes, but it's the worst thing you can do. There are different users with different permissions in your OS. And that is on purpose. Giving root permissions to your user permanently will compromise the security of the system. (Remember Windows 9x and all the viruses ?)
Executing a command with sudo wont need any of your customization stuff I guess, unless you execute /bin/sh (a shell).
To achieve what you wanted you can do the following:
You can move your stuff from ~/.bashrc and ~/.profile to the system /etc/bash/bashrc and /etc/profile, or even better put them in separate script in /etc/profile.d/mystuff.sh (dont forget chmod +x /etc/profile.d/mystuff.sh). These files will be executed for each login session.
Then start a root session with su -, the - (minus) sign passed to su will execute a login session and therefor will execute the files mentioned above. Depending on your linux distribution you may need to call sudo su - instead.
Once you finish with the root session, it's good idea to logout and leave the root permissions.
There is another way if you need root permissions only for specific binary, it's called Effective UID. For example you may use this for mtr binary:
chmod a+s `which mtr`
This way when you execute the mtr binary it will get effective permissions of the user who owns the binary - root in this case (chown root /path/to/mtr). It will save you the sudo typing, but you should carefully choose which binary you will give root permissions. It's dangerous if you do not know the risk. Better use the first option.