No, you do not. The full rules for psionics–magic transparency make no mention of prestige class requirements, nor do they include any rule general enough to cover them.
Under psionics–magic transparency, the following things are transparent:
- Spell effects
- Power effects
- Magic item effects
- Psionic item effects
- Spell Resistance
- Power Resistance
- Dispelling magic
- Dispelling psionics
- Detecting magic
- Detecting psionics
- Suppressing magic
- Suppressing psionics
Nothing not on this list is transparent. That includes the requirements of not only prestige classes, but also feats. Likewise, the effects of feats and prestige classes are not transparent either—unless the effect of that feat or prestige class is one of the above things (e.g. a prestige class giving you some spell resistance). So even if you could get into thrallherd (e.g. Hidden Talent feat, maybe), you would not able to apply its manifesting advancement to druid.
Another thing that isn’t transparent is the specific spells and powers themselves, even if their effects are. So Rary’s telepathic bond does not count as mindlink for thrallherd’s requirements, even though the effects of each are pretty similar.
Finally, all claims above are made ignoring the magic mantle from Complete Psionic. The magic mantle’s effect is, arguably, to cause even greater magic–psionic transparency—but it is hideously vague and no one knows what it actually does.1 It seems likely (based on “Most campaigns already treat them in this manner”) that all it really does is (or at least, is meant to do) is allow magic–psionic transparency in campaigns that aren’t otherwise using it, but the statement of the effect (“you always treat magic and psionics as identical”) is, taken on its face, a far stronger statement than the usual magic–psionic rules from Expanded Psionic Handbook. In any event, without dipping ardent or (shudder) divine mind, you aren’t getting the magic mantle anyway.
- This section is referring to the second paragraph of the magic mantle’s granted ability. The first paragraph, making Use Magic Device a class skill and refunding skill points spent on cross-class Use Magic Device and/or Use Psionic Device, is clear enough, but not relevant here.