Yes, you can show a coupon in any widget area such as a sidebar or footer.
In current versions of WordPress, widget areas use blocks. Go to Appearance > Widgets (or your theme's widget area in the Customizer), add a Shortcode block, and paste your coupon shortcode into it:
[coupon couponid="1"]
If your theme still uses the classic Text widget, WordPress does not run shortcodes inside it by default. You can enable that by adding one line to your theme's functions.php file (or a small functionality plugin):
add_filter( 'widget_text', 'do_shortcode' );
After that, the coupon shortcode works inside a classic Text widget as well.
Keep in mind that sidebars are usually narrow, so a full-size coupon may look cramped. You can set a smaller display size with custom CSS, or use an image coupon sized for the space. For general placement help, see Where does the shortcode go?.
