All of the themes on the Shopify theme store are made to be responsive -- meaning they should look great regardless of the type of device used to view the site (ie. desktops, laptops, tablets, and phones).
However, before you pop the champagne at your launch party, you should definitely make sure you've tested out the site on multiple devices. Try to get your hands on as many different computers, tablets, and phones, using as many different browsers as possible: Google Chrome, Safari, Internet Explorer, Firefox, Opera, etc. Vigorously test your site by using these various devices and browsers to navigate through your site.
If you're having a launch party, I recommend getting everyone to bring their phones and/or laptops, then having at least 10 minutes or so, where everyone can browse your site and report any issues or errors they find.
It's better to find out about any issues before spending lots of money on advertising campaigns and marketing. You don't want to be sending customers en-mass to your site, if a large percentage of them are going to have issues.
Test, test, test, and test again. As with most things in this guide, it's better to be safe than sorry.
Need more help with this step? Check out Quirktools' free browser-based app, Screenfly, by clicking here.