A boost pedal won't turn your bass into an active bass. An active onboard EQ is what does that. An active EQ has both cut and boost adjustments with straight up being flat (no boost or cut to the signal).
Passive bass EQ's are typically all cut because they don't have any power to boost it. Like my passive Jazz bass. If it turn the tone knob all the way up, it puts out everything my bass puts out. If I cut it to halfway it's a lot bassier sounding because it is cutting out the treble signal from the bass. With an active bass you usually have at least two or three tone knobs (bass and treble, or bass, mids, treble) and besides cutting the signal from any of those you can boost them because you have batteries powering your active onboard preamp.
You don't have that ability with a passive bass. If you have more tone knobs on a passive bass, you can have finer control over your sound, but that doesn't come by boosting any of the frequencies. Instead it is cutting the ones you don't want to use. If you add a "Boost" pedal, all that will do is give you a stronger overall signal or perhaps add overdrive and distortion with it. It won't turn a passive bass into an active bass because it won't turn you onboard bass EQ into a cut/boost EQ, it just boosts the signal of whatever you passive bass is putting out.
My primary bass is a passive Jazz and my inexpensive 5-string is active, but can also be played in passive mode. In active mode I can boost or cut the bass or the treble, plus I can balance between the two pickups (Jazz style neck pickup and MM soapbar style bridge pickup). In passive mode I only have control over the the pickup balance and nothing else. That's OK with this particular bass because if I need more treble, I'll adjust the balance a little towards the bridge pickup. If I want a darker sound I'll adjust the balance towards the neck pickup a bit. I actually usually play it in passive mode because it sounds better and the adjusting the tone by adjusting the balance between the two pickups works fine. Like I mentioned above it's an inexpensive 5-string and although it works fine for the few times I need to use it, it doesn't really have the really nice preamp that a more expensive active 5-string does.