As someone who biked from my front door and back I'll offer my thoughts.
How well have you thought about this?
There's more to cycling in a foreign country, carrying all your gear than you might have experienced on your vacations.
How will you carry your gear? (You may be able to have it shipped daily).
Will you stay exclusively on the road or are you able for some of the Camino rurales?
How are you for basic bike maintenance such as punctures?
You do realise that you will "lose" whatever contacts/relationships, the "Camino family" as soon as you ride off into the sunset? And then will be starting from scratch further along the road?
The body is used differently walking and biking. Long days (for you) on a poorly set up bike (cyclists pay as much attention to saddle and set up as hikers do to footwear) may impact on your walking when you resume. Or vice versa.
I say all that not to put you off (exploring new places on a bike is a fabulous way to travel).
But this worries me...
I think you should be riding your bike because you want to - not because you have to.
I think this is the crux of your issue.
I'd urge you to consider alternatives such as where you start, how you travel. Or, indeed, where you finish.
It took me 15/16 days SJDPP - Santiago, on a bike (very slow) and I wish I had done it slower.
If this is a once-in-a-lifetime chance and Santiago is a goal then perhaps start closer. If not, perhaps consider this as "stage 1" and go as far as you can or wish and return at another time.
Or else do the whole thing on a bike and get to see and explore so much more than you would have on foot. Or just have the time to stop and appreciate the roses (or vino tinto!
)
Whatever you choose I'd suggest in taming the big clock that is ticking over your head.
Good luck!