Can you run a single 2ohm dual voice coil sub and a single 4ohm DVC sub off a single mono amp?

It depends on the amplifier. If you absolutely want to leave the current subwoofer configuration as 2ohm and 4ohm, the resultant impedance seen by the amplifier is as follows:

Both wired In-Series:

2ohm + 4ohm = 6 ohms

Both wired In-Parallel:

1 / ( (1/2) + (1/4) ) = 1.3 ohms

The Parallel configuration can probably be only run by a 1ohm-stable amplifier whereas the 6ohm Series configuration can be run by any amplifier that is able to drive anything under 6 ohms.

Also if ran in the Parallel configuration, this mismatch in driver impedance may also cause the 2ohm subwoofer to receive more power, resulting in a different sound characteristics than the 4ohm subwoofer.

Usually with DVC subwoofers you want to match the impedance between drivers. If possible, configure each subwoofer to 4ohms and connect them in Parallel. This will produce a total impedance of 2 ohms (you need a 2ohm-stable amplifier). If your DVC subwoofers only support 2ohms and 8ohms do either:

Both wired In-Series - configure subwoofers to 2ohms:

2ohms + 2ohms = 4ohms

Both wired In-Parallel - configure subwoofers to 8ohms:

1 / ( (1/8) + (1+8) ) = 4ohms.