Adding sheathing under a concrete tile roof

I wouldn't worry too much about it. The plywood is not typically supporting a load of more than the paper and asphalt shingles that were placed, even more so if you have a considerable pitch on your roof to where it would be difficult or impossible for a person to walk on. It basically serves so that you have something to nail the shingles down securely.

Most newer homes use plywood, I have an older home that used what looks like rough cut deck planks and those are mostly still original. The last time I had my roof replaced, they had to change out a few boards that were terribly dry rotted and some that were badly damaged from previous water damage by the oh-so responsible homeowners who had the home before me. Other older boards look noticeably damaged by the most recent nails but they continue to hold down the shingles and I would still feel safe to stand on my roof.

As long as the shingles are doing their job then the plywood will not be exposed to any water, and as long as your attic has good ventilation during the summer time then you should have nothing to worry about for the next 15-20 years at least.

Skip sheathing for shake roofs used to be really common around my area of the country and I've never removed it (or seen anybody else remove it for that matter). OSB or plywood over skip sheathing makes for a much stiffer roof deck, resists problems with expansion better, and obviously doesn't require all the hassle of removing it.

After you strip the roof, do spot repairs to the existing sheathing where needed, then go right over it. You'll want to use both longer sheathing nails and longer roofing nails. The sheathing nails should be long enough to give a good hold in the studs, and the roofing nails should be long enough to penetrate both layers of sheathing.