Is it a bad idea to daisy chain to an internet router through an external drive?
No, there will be no significant performance loss, if any. The reason is that Thunderbolt is a low-latency, 10Gb/s (minimum) connection, which is far faster than the gigabit speeds you get from the adapter. Thunderbolt will have to wait for your ethernet adapter, not the other way around, which is exactly what you want.

If you're worried about the hard drive taking up some of the performance, keep in mind that the first iteration of Thunderbolt (the one you have) was designed with two lanes. Each device will utilize one of those lanes, and have complete access to dedicated 10Gb/s performance.