The answer
They can if the chain charges for transaction size or verification work, although compression, batching and protocol choices change the outcome. A blanket price prediction is not justified.
What to do next
Compare real signature byte sizes and the chain's transaction fee model.
NIST Post-Quantum Cryptography resources
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Trezor hardware wallet
A current-generation hardware wallet for managing keys; it does not make Bitcoin or Ethereum quantum-resistant or resolve a future protocol migration.
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