Hmm no replies?... Here are my thoughts, now keep in mind I have never heard the Dragonfly, but I did demo the LD1 (or 1+ I can't remember) a long time ago.
My understanding of the Dragonfly is its a low impedance headphone circuit, low voltage and overall very good at delivering current peaks. Which makes sense for its overall size and with 5V/.5A coming in from the USB (theoretical ~2-2.5V max swing in both directions). So its perfectly suited to drive your Grados and similar low-Z cans.
So its questionable (on paper) if your Grados would benefit from additional amplification gain stage.... from a pure signal gain standpoint, disregarding the even order harmonic "coloring" effects of tubes for a second.
The X-factor is how the Dragonfly sonic character will change with the increased impedance load presented by the headphone amp. You'll probably have to do some in-depth searching for that answer. One thing I have found is high voltage amplification circuits (IE circuits capable of delivering "bigger" voltage swings than current swings) benefit GREATLY from high impedance loads presented by the next downstream component. It can be a night and day difference in this regard, and I think a lot of HF forum "amp hype" really stems from impedance matching of components.... as much as the additional amplifier gain stages.
Tubes DO make a difference. No doubt about that. So disregarding everything I have mentioned thus far, adding even order THD to your system will make a difference. It will also open up the fun of tube rolling, burn-in, tube psycho-acoustics and all that old school fun. Although my understanding of the LD1+ is its a relatively low % even order harmonically distorted circuit. Its one of the "cleanest sounding" tube circuits I have heard. Thats kind of why I chose a Millet hybrid over the LD1, the Millet bias voltage can safely be increased/decreased to dial in or out more even order THD. Thats a really unique feature of the Millet deigns that I wish more amp makers would implement.
Hope this helps... good luck in your search, and welcome to HF, sorry about your wallet.