I do not know what the effect will be on Fe3O4 nanoparticles, but I already have seen for other particles that there can be an effect agglomeration wise. You will find in publications on TiO2 that by the use of NaOH and KOH platelets of TiO2 will form nanotubes or nanofibers depending on the used base. I also have seen it for materials I use (this will normally be published soon). This offcourse was not used in a coprecipitation method. The only way to know if there is an effect, you can try both off course.
You may need to be carefull with NaOH as base, because for some applications (I do not know for Fe3O4) it can be important to exclude ions like Na+, K+ because they will sit in interstitial sites of the material and thereby contaminating the material. If this does not matter for your material, than discard this last part.