I got this question from a coworker, who has Nexus 4, which uses Broadcom NFC chip.
The answer is yes & no.
Broadcom doesn’t support Mifare directly. It only support NFC Forum Type 1-4.
Since NFC_FORUM_TYPE_2 includes Mifare UL/UL C, Broadcom NFC chip supports Mifare UL via NDEF, not raw read/write. The same situation applies to NFC_FORUM_TYPE_4, which includes MIFARE Desfire. Thus, Broadcom supports Mifare Desfire via NDEF, not raw read/write.
Since Mifare Classic is not part of NFC Forum Type, Broadcom NFC chip doesn’t support it.
If you are in market for NFC tag, to ensure compatibility in all phones, don’t buy Mifare Classic.