Headcount? On a widebody? not these days.
Most airlines have the barcode scanners to do that job, in 13 years I only ever did a headcount on planes under 50 pax, when remote boarding or when there were unaccounted for pax and the numbers didn't add up.
On a widebody, at a modern airport jetbridge with barcode ticket scanners, the responsibility is on the gate staff to match the count.
The crew at the door do check tickets yes, but with the way pax rush on like stampeding cattle and snatching the stub away barking their seat number, you're lucky to get a proper look. Personally I used to get a hold of the boarding pass and not let go til I could properly check it, but not all crew are that assertive. There could also be cultural issues or inexperienced crew in the equation too.