Sure! It just depends on how complex the graphics you're going to design are. The larger the file, the longer it will take to process. The more special effects, layers, etc., the longer it will take to process. The issue with smaller laptops isn't necessarily that they can't be used to produce graphics, it's the efficiency - the speed which it takes to render something. Larger laptops with more RAM (6 GB or more) or better graphics support have no problems with graphics. Smaller ones (under $300) will be slower.
Take a look at the version of the graphics package (Photoshop, Illustrator, etc.) to see the minimum requirements then compare with your own laptop. If your laptop appears to exceed the requirements, you can be comfortable running the graphics software. Still not sure? Go to the manufacturer's web site, download a free trial of the software, install it, and play around with it. Many offer 30-day trials to let you make up your mind.