Is it permissible for the Asr prayer, which began a few minutes before the Maghrib call to prayer, to have another worshiper join it at the very moment of the Maghrib call to prayer?

The prayer is valid. It is considered performed if one rak'ah is caught before the Maghrib call to prayer, and it is considered a missed prayer (qada') if the Maghrib call to prayer occurs before one performs a single rak'ah of it. This is based on the saying of the Prophet, peace and blessings be upon him: "Whoever catches one rak'ah of Asr before the sun sets has caught Asr." It is not permissible to delay the prayer beyond its prescribed time without a legitimate Shar'i excuse. The Prophet, peace and blessings be upon him, clarified that this is characteristic of the prayer of the hypocrites.