Can my phone get blacklisted even if it has been unlocked?

The answer is YES.

So, what did the unlock do?

The unlock lifted any Network Carrier Locks the device had.

Example:

A T-Mobile phone that restricts any other sim card not supported by the T-Mobile, this is considered a Network Carrier Lock which the Unlock lifts. Therefore, when an unlock has been performed, it may now accept other sim cards such as Sprint, AT&T, Verizon & so forth.

The unlock, however, does NOT remove any payments owed to the company the device pertains to. In the example above, if the device is from T-Mobile, any payments owed to T-Mobile still remains on the device, as does for any other carrier respectively.

If your intention is to unlock a device and NOT pay off any bills owed, then you may run into the company blacklisting your device; in which case, if it does happen, the Unlock still remains on the device but it will no longer pick up signal from any carrier belonging to the same country it was blacklisted in. If this ever happens, you may still use your device (as it is still unlocked) any where else in the world except the country it was originally blacklisted in. In the example above, the T-Mobile device may still be used outside the USA, but will never pick up signal inside the USA. The same is applied for any other carrier in their own respective country.