If all the miners colluded, it could potentially ddos, but then there will of course be a countermeasures taken by users and honest miners.
I just think this is a pure attempt at fud to convince people to sell bitcoin and buy shitcoins.
Discussion
These news tend to come always at times when bitcoin is pumping.
If the ordinals are just used organically, at worst, the blockchain will have some non-transactional spam taking up parts of some blocks, and fees might become temporarily increased if there is heavy congestion. I belive the fee market will sort that out.