Not as a rule.
Of 740 serviceable Bf 109s on 31 August 1940, 307 were Bf 109 E-1s, 103 were E-3s, 304 were E-4s and 27 were E-7s.
Some of the E-1s might have been converted to cannon, that would be difficult to ascertain. They should have had the designation changed, but we know that did not always happen. Conversion from E-1 to E-3/4 standard was not a job that could be done in the field.
The 100 E-1s delivered up to the end of September were accepted and delivered as E-1s. I find it difficult to believe that these were cannon armed. They would not have been manufactured and accepted by the BAL under the specific designation E-1 if they were. Remember that the E-1 and E-3 were being produced concurrently, there is a reason for the different designations.
Bergstrom has calculated that roughly 40% of Bf 109s flying in the BoB were armed with just four machine guns.
Edit: I just checked. Exactly one He 112 flew in Spain, three in Hungary, at most twenty four in Romania. If that's 'entering service' so be it.