Having a strong signal going into a DI is a plus, but the concern is that you get some high end bleed off similar to how you can with long cables. A basic active DI box is basically just a DI with a buffer (not talking about tube DIs and what not). So if your signal is buffered some other way, you should be fine.
Frankly I think it's a little overrated, but I'm not big on an overly bright bass signal to begin with. I've done church gigs on and off for years at a variety of churches and I don't think I've ever seen one with active DIs. And they've all survived for years with players bringing everything from cheap Squier P basses to nice active Stingrays and such.
I'm all for a good EQ/DI combo, but I will always leave a passive Radial in my bag just in case all else fails.