The T20s are driven perfectly fine by the iPhone itself, and that headphone adapter that comes with the iPhone 7 is already pretty good by all accounts. One thing you need to remember is that if you have the T20i variant then the inline controls will no longer work, and nor will you be able take calls using the T20's microphone.
IMO the main reason for buying a Dragonfly, or something like it, is to enable the use of relatively difficult to drive headphones with a laptop or mobile device. If the headphones that you're currently using are already driven well by your existing source then really the only difference is likely to be a slight change in tonal presentation, which you may or may not like.
IME The Dragonfly, really comes into it's own with headphones that need more oomph than the inbuilt headphone port can supply. The difference between the Dragonfly and my iPods built in headphone port is night and day with my Beyerdynamic DT1770 Pros, with the Dragonfly producing a far more dynamic and detailed presentation, whereas the output from the iPod is pretty lifeless. With other headphones that the iPod already drives fine then there's very little difference.
I suppose a general rule of thumb is that if you need to push the volume level of the source device beyond 75% to get an adequate listening volume then you should consider a Dragonfly. If, on the other hand, you already get a perfectly listenable volume at 50% - 75%, or less then the Dragonfly is unlikely to make a night and day difference.
It's not just about volume though, it's also to do with the dynamics. Powering a headphone that needs a high volume setting from the source is likely to be lacking in dynamics and will likely sound flat and lifeless in it's general presentation, and this is where the Dragonfly (or any external DAC/Amp) comes in. With more power on tap it's able to do a better job of controlling the headphones drivers at equivalent perceivable volumes leading to a more dynamic presentation.
I do think that people really need to consider exactly why they need an external DAC/Amp, because it may not be the magic bullet that you're looking for depending on your headphones. In fact I'd say if the headphones you have are already driven fine by your DAP, then it's likely that looking into upgrading your headphones will bring more to the table than an external DAC/Amp will ever do.