Yes, you ay run into problems, buying an iPhone in Europe.
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Apple may restrict warranty service for iPhone, iPad, Apple TV and HomePod to the country where Apple or its Authorized Distributors originally sold the device.
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RESTRICCIÓN IMPORTANTE PARA EL SERVICIO DE iPHONE, iPAD, Apple TV Y HOMEPOD:
Apple puede restringir el servicio de garantía para iPhone, iPad, Apple TV y HomePod al país donde Apple o sus Distribuidores autorizados vendieron originalmente el dispositivo.
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copied from: Legal - iOS Warranty ALAC Spanish - Apple
Also, the built in hardware may not support your local carrier network.