No, you need to connect the PSU to the SATA power connector (presuming it's an 'in' connector same as on SATA devices). USB (especially 3.0) is able to provide good amounts of power to connected devices, more than the PCI-E bus can safely provide, so power connectors are placed on the USB cards to fetch this power from the PSU.
They used to have Molex connectors but as SATA became more common on PSUs it's becoming more usual to use SATA instead.
[[Double] Edit] Ah, on reading your post again I think you understand this and are just asking if it will work without the connection. It depends on the card, but it ought to. Just be very careful about what you connect.