I see that the Teensy 3.2 is "5v tolerant," but it's not entirely clear to me if its GPIO can also drive a TTL device, or whether I'd need a level converter for that.
You have to look at the datasheet. Things using real TTL logic levels are fine. CMOS stuff running at 5V Vcc often requires 0.65-0.7 Vcc for a logic high, which is an issue.