Adding ASCII art to the source code (the HTML files) may not interest people who don’t look at source code.
The source code is an easy place to add ASCII art because those files open in plain text, no formatting or fancy fonts. So, the ASCII art shows up without much extra work, almost none in fact.
If you access your HTML files you can add ASCII art yourself, without the plugins. (See above). But, not everyone wants to do that.
WP Figlet is all about adding text created in ASCII art fonts (figlets). It even lets you choose which figlet fonts you want to use. The auto suggestions creates a figlet in your source code like this (you choose your own words):
It does work.
Source Code (although not updated in 4 years, also works). If you are timid about mucking around in the HTML files then either of these plugins will work for you. Source Code lets you choose to have the ASCII art in your header or footer. However, I found it did need the extra HTML code for keeping the formatting after I saved my text image.
One thing I dislike about Source Code is the lack of artist credit (artist initials). I checked several of the ASCII images available with the plugin and none had artist credits. I used my own ASCII image with my initials.
In the end… DIY.
Don’t be bashful about getting into your own source code. Skip the plugins and just do it yourself. Once you access the file it’s very simple to add the ASCII art with the code for notes. (See the first image in this post, no reason you can’t do that yourself).