It is possible to search the blockchain for other certificates that the learner may have received, but the content of these certificates will be encrypted.
What we learned from designing an academic certificates system on the blockchain
MIT Media Lab
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This is the case if and only if certificate issuers send ‘proof of learning/credential’ transaction data to a singular learner address, correct? While a learner may wish to only use only one public address for accumulating credentials on the blockchain, it seems to me more likely that they would have many assembled over the sum of their academic and informal learning experiences. The sum of these addresses could be assembled in a wallet, which could be selectively exposed by the learner at the times and situations of their choosing.

I suppose that most credentialing organizations/entities would likely use a singular transaction address per learner, but not necessarily.

Having one public address for learning credentials would in essence entail the creation of a universal and permanent student ID, which I suspect many would not feel comfortable with. It certainly raises privacy concerns.