Yes, you can mix an image and text in the same coupon by adding a little HTML to the coupon's deal field.
The free plugin does not give the deal (discount) field a visual editor, so to place an image alongside your text you write the HTML yourself. For example, you can add an <img> tag pointing at an image in your Media Library next to your headline and terms. Copy the image URL from Media > Library and drop it into the field like this:
<img src="https://example.com/wp-content/uploads/logo.png" alt="Logo"> Save 20% this week!
If you want richer layouts without hand-writing HTML, Coupon Creator Pro adds column and row layouts plus a visual editor for styling the content, which makes side-by-side image-and-text coupons much easier to build.
For the basics of building a coupon, see Creating a Coupon; for image-only coupons, see Creating an Image Coupon.