Richard, I biked the CF in 2015 and as stated above, it is doable and you can receive a Compostela.
A few thoughts....
You have a choice of following the roads or the route followed by the walking pilgrims, or indeed a pick'n'mix of the two.
If following the "walkers" path, it may not necessarily be much quicker. Progress is (and should be) slow because of the surfaces and the walkers.
Think about baggage. You certainly do not want to cycle with your backpack on your back. You'll need to strap your backpack to your rack, or better still use panniers.
Cycling is not necessarily "easier" than walking - just different. The advantage of a bike is exploring off the route and being able to make up time. No room at the inn? Not too much of a problem on a bike. (Remember, some Albergues will not accept bikers until later in the day). There are some big climbs (followed by big descents!) but the ride is doable by anyone with a reasonable degree of fitness, especially if not in a rush. But on a rented bike, expect a sore ass and other aches and pains.
Rain gear that is effective for walking may not be so effective on a bike. Riding in the rain can be glorious! but it can also be miserable if you're wet and cold.
The only "extra" gear you need is cycling gloves to protect your hands in case you fall. Padded shorts are not necessary unless using a racing style saddle - unlikely on a rented bike and easily changeable in any case.
If you haven't ridden a loaded bike in a while, do it before you go. You'll be riding in close proximity to people and in some busy places. Your safety and the safety of others depends on you being able to control your bike with a load, sometimes at low speeds, and sometimes at very high speeds!!
Be able to do basic mechanics such as brake and gear adjustment and fix a puncture (less of an issue if you stay on the road).
And the biggy! Because you'll move faster and longer than walkers, there is a danger that you'll miss out on the more social aspects of the Camino. If you start off walking and subsequently pick up a bike for a few days, you'll be leaving your "Camino family" behind. And if you resume walking again, you'll be starting off the process all over again.
I met one girl on the Camino who started on a bike, sold it and continued to walk. She preferred the walk.
Walking is not an option for me, unfortunately and I loved my biking Camino. But I was on my own bike, had toured several thousand kms before I started and was in the fortunate situation that I was in no rush.
Personally, I'd think it would be better to choose one mode or the other. Aches and pains from walking after a week or two may make riding a bike more difficult. And vice versa. A rental bike will take time to get used to depending on how familiar you are with carrying a load. A bus will allow you to make up time if you are under pressure walking.
Spain is fantastic for biking. If you do want to bike, I'll give you the same advice I got from a bar-tender in Santiago - head west and enjoy the coast! He wasn't wrong!