Bumping up this question.
I have tested this with net-snmp and it seem to be able to handle the (according to the RFC) max Counter64 value:
he Counter64 type represents a non-negative integer which
monotonically increases until it reaches a maximum value of 2^64-1
(18446744073709551615 decimal), when it wraps around and starts
increasing again from zero.
So a Counter64 value is BER encoded as an INTEGER however it has a subtype constraint on the value. ASN.1 is a specification language. The above says that an implementation of the protocol should BER encode an INTEGER for transmission but internally limit it’s use to values between 0 and 18446744073709551615.