Hi there.
I haven't used that specific plan, but I did follow a similar one back in 2008/09 when I was training from absolute scratch for a half marathon (I'd never run any kind of serious distance before that).
I found that it worked really well for me in terms of building the stamina that I needed, because the walking does give you the breaks you feel you need (mentally as well as physically), and these gradually get shorter as the running periods get longer.
I stuck with time, rather than distance, as my measure; that way, you get to jog at your own pace. Just make sure you try to stick consistently with three sessions a week and do take water with you. Might be better to train at a cooler time of day, too.
I ultimately managed my half marathon in just under 2 hours, so these programmes do seem to work. Best of luck! :sport: