The answer to your question is yes..... and no. Yes you can do that but it isn't nearly as straight forward as you may have been lead to believe. There are a number of "gotchas" that will have to be dealt with. If you aren't very familiar with Linux the practical answer to your question is no.
I have a better solution to your problem. Make a text file of all the programs you usually add to your new installs and just paste them into a terminal and do them all at one time. Unless you have a very slow connection, ie dial-up, it shouldn't take that much of your time.
Below is a sample of what I mean. I just copy this from a text file I keep for update notes into a terminal and hit enter, put in my password, hit enter again, and watch them all download and install while I have a piece of home-made pecan pie and a cup of coffee.
sudo apt-get -y install armagetron kmahjongg pingus neverball wesnoth bzflag flightgear xpilot-ng tremulous planetpenguin-racer lbreakout2 oolite torcs scorched3d wormux nexuiz openarena vegastrike supertux freeciv chromium airstrike lincity-ng supertuxkart xmoto uqm koffice opera checkgmail scribus-ng scribus-ng-doc kde-extras kdeaddons kubuntu-restricted-extras kcontrol kcontrol-autostart firefox k9copy ubuntu-restricted-extras synaptic gimp gimp-data-extras gimp-help-common gimp-help-en xmms-kde mplayer mozilla-mplayer inkscape kmymoney2 ofx xchat picasa libnet-google-perl libnotify-bin miro w32codecs libdvdcss2 libdvdcss mplayer-doc ladspa-sdk googleearth
As you can see, I would grow old...er trying to install all these one at a time.
EDIT: Don't try to use the list I have above. It is for Kubuntu, not Mint. There are some things in there that will bork your Mint install.