>The only value listed is Hfe = 200.

Beta of 200 then.  (I'd design to 100, if I was you :)


>I think I see what you're saying. The load is a relay coil and when the input
>is +5, the relay isn't on. Is it still possible that Q2 is conducting but
>just not enough to trigger the relay?

In this circuit, with two NPNs, it takes a low at the input to turn on the
relay.
Low in turns off Q1, then the current through Rc has nowhere to go except
through Q2's base.
If Rc isn't small enough, then Q2 may not conduct enough current to pull in
the relay.

Don't forget that protection diode across the relay!

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