SPIT, your terminology is a bit unclear.
Are you saying you have a computer which uses a dial-up modem via a telephone line to log on to the internet via your web browsing program?
If not are you using an ADSL modem, the type that has a single USB plug which plugs into your computer?
If either of the above then yes duplicating the settings will give access to the internet. That access can then be used by ANY web browsing software on the laptop e.g. Internet Explorer, Firefox, Chrome, etc. to access any web site. If she wishes to access YOUR web based e-mail account she will need to go to YOUR provider's website and log in with the appropriate username and password.
If you both have computers and wish to use them at the same time for using the internet and you have an ADSL modem then you would be better to replace that modem with an ADSL wireless modem/router. That will handle the connection and allow both computers access to the internet individually or both at the same time. The advantage also is that yoru wife's laptop should be able to connect using a wireless connection.
I hope the above makes sense but keep asking if unclear and advice will be forthcoming!