I was wondering if I plugged my bass into a DI/Preamp like a Sansamp Bass Driver or a Hartke VXL Bass Attack directly into a PA would sound any good, cause I already have the PA boxes and I can't afford a amplifier, just a DI box
Hi how are you?
it all depends on the PA if it'll sound good. My one amp's built-in DI doesnt even take the signal through the preamp or anything so its exactly what you'd be doing, it sounds good though through our PA and everything. Just be sure to EQ it on your mixer
Guitar Rig:
Fender Telecaster
Martin GPCPA5
Orange Rockerverb 50

Bass Rig:
Squier Vintage Modified Jazz V
Hartke HA3500
The PA has to be decent. These types of stompboxes are designed for use without an amp also. I recommend the Tech 21 or the MXR Bass DI Plus.
I use the MXR Bass DI thru the PA np and sounds great. Sometimes I'm just too lazy to take my cabs, lol.
Schecter Stiletto Studio-4 (both in see thru black)
Schecter Blasko Bass
GK 700rb ii
GK 4x10 cabs
MXR M-80 D.I.
MXR M-182
There's two answers to this.

You say you can't afford an amp so I don't think we are talking a big top flight PA. If the PA is good it will handle bass, especially in a rehearsal room where the PA is pointing at the band. At a gig you need some speakers pointing at you because you need mids and tops to hear what you are playing. If you have good monitors this is perfectly good enough and loads of professionals do just this. It does mean that the sound man controls your sound though.

very few bands have a PA good enough for this. Bass is very demanding so you are going to need subs on the PA and beefed up monitors on stage. I take my bass stack with me to most gigs and leave the subs at home because the subs take more effort.

Most people find it better to take their own back line to a gig. Most bands will expect you to have your own amp. There's no reason why you shouldn't use the PA at rehearsals however so long as it is not thrashed.
You can but you won't have any foldback (right word?), so you won't hear yourself very well, and it'll be put to a mixing desk which means you don't control how you sound.

but at the same time i doubt it will sound really great
As everyone else has said pretty much: It depends, but don't rely on it being consistently good. I've played DI a few times, and its been really well done some times, and really poorly to the point of having to ask to use another bands bass amp mid-set because the sound guy wasn't helping me at all. You just need to make sure you sound check properly beforehand.

Acoustic basses and double basses tend to sound pretty good through a DI though.
if you want to do this live and know/trust the sound guy and can properly sound check before then it can turn out really well. i have done it a few times with my sansamp BDDI, and it sounded great.

however, as has been said before you won't be able to hear yourself very well if at all, because the bass is normally mixed very low in the monitors to stop it muddying the vocals.

what i would say is the best idea is to look for a used combo amp with a DI, so that you can go through the pa, but still be able to shape your sound a little as well as being able to hear yourself. you can pick up some nice used DI combo amps for about 150-200 dollars.

i would say it is worth saving up for the amp over a DI box to start with.
My Setup:
Fender Aerodyne Jazz Bass,
Fender USA Jazz Bass
Hartke LH1000,
Hartke Hydrive 410,
Sansamp BDDI,
Electro-harmonix Black Finger Compressor.