Yes, this is the way it works. There are several guard houses. The one Nunes probably used is on the west side. Members of Congress do not have carte blanche authority to come to the WH whenever they want and just wander around. Not even Cabinet members have that right.
At each guard house, secret service officers have a list (updated in real time) of non-White House staff who have been given permission to enter the complex for a specific purpose. For each such person, there is also the name of the White House staffer who has given permission; the expected time of arrival; the person they are meeting with; and the room number or name.
The meeting will eirher be in the White House, itself (yes, the West Wing) or the much larger Executive Office Building right next door, separated from the WH by a small outdoor parking lot. The visitor is then directed to a lobby area in the aporopriate building where the person waits until the WH staffer (or his secretary) who invited him comes and gets him. When the meeting is over, they are escorted back and out of the complex.
There are always a few people who have been given what in the old days were called -if I remember correctly - A-Passes, which gave them permission to come and go as they please, even including the residence. But, as you would guess, these passes were always severely limited to family and a few very close friends. The possibility that Nunes had one of those passes is less than zero.
So, you are right. There would certainly be a record of Nunes’s meetings at the WH. The Democrats should demand to see it and subpeona the appropriate WH staff and Secret Service guards who handled his entrance and exit.
Hope this helps.