How successful you are depend on two factors.
First, how long your zucchini producing season is. Around here they produce like crazy for one month, then start slowly declining and after another month or so the plants are ready to be pulled because they are completely spent. No point bothering with a support for so short a season.
Second, what cultivars are you growing. Some modern European ones (Eros, Ortano, Striker etc) tend to have a growth that lends itself well to being grown on a support. Or so the brochure says.
I generally grow one of these cultivars since they are all superb producers and extremely virus-resistant, and I've experimented growing Striker on a support last year. I won't bother again.
When plants have been producing for about a month they become so large and heavy they need a hefty support, and that's to get one extra month of declining production before pulling the plant. I just let them run on the ground for that.
There's also the question of what you are growing. I have grown some heirlooms over the years and apart from one (Doentsky Bar from the Donbass) I have never been fully satisfied with them. Since switching to modern cultivars my production has increased dramatically (and with this new foliar fertilizer I am trialing it has increased even more) and I have to toil far less to remove dead foliage and to keep an eye out for viruses: the only problem that requires careful monitoring is Powdery mildew.
Yours look young but are already heavily pruned, so I take you are growing some heirloom, right?
