The only way you could get a type rating on a US Airman Certificate without having to undergo testing is to apply for a Private Pilot Certificate on the basis of your ICAO license. The type rating will transfer across but will contain the limitation that your ICAO license must be valid in order to exercise its privileges. The Type can only be used for Private Pilot privileges in that case.
If you already have an FAA ATP, then you will need to take the Type ride with an FAA examiner to put it on your FAA ATP.
14 CFR 61.41 only applies to training given and endorsements, not the transfer or conversion of any licenses or privileges.
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