Hi there
Date of birth isn't included, though age will be - although you can see that in any case from the GRO index, which shows age at death.
However, the validity of the information is down to the knowledge of the person telling the registrar.
And therefore it may be correct, or in fact could be well out.
You can see from the 1939 Register that many people either don't know their OWN date of birth (as compared with the evidence of a birth certificate) or choose to alter it for a variety of reasons.
So if you're wanting an idea whether a death is yours or not (so to speak) then comparing a known age with what the informant said to the registrar, and shown on the GRO index, will be as good as buying a death cert.
On the other hand, the informant, the address at death, the occupation of the deceased, and other details on the certificate might be good clues?