It depends where the signal gets delayed. Is the GR-33 a slow or a fast converter? Is the MIDI interface slow or fast? Both, the converter and the MIDI interface are responsible for the time from picking the string to recording the note. For example: I felt a remarkable difference between my old Roland GR-20 through a Motu MIDI Express and the Axon 100 through an Emagic AMT-8 I use now.
And there is the plugin delay. All plugins need processing time, some more, some less. Now think about the whole chain. Audi-to-MIDI conversion in the guitar converter (time), MIDI transfer (time). Entering the computer and Logic (time), processing the sound (time), sending the sound out from Logic through the computer through the audio interface to your speakers or headphones. Everything needs a little time and under bad conditions and depending on your playing you may run into an unplayable situation.
And there is more: Deep tones are harder to convert than high tones. The wave length is longer at deep frequencies and this results in longer processing time in the converter. To avoid this you can play one octave higher and set the softsynth one octave lower but apart from another string sound this is just an example, you have to optimize your chain in every stage.
From my experience and with the gear I know it is hard to play exactly in time with a guitar-to-MIDI converter and software instruments. The more you are able to play a little before the real time, the more precise the recording is. But it will never be as accurate as hearing the sound from the guitar directly. I am quite used to that kind of playing but I always feel like wading through honey and can't get the right feeling.
One solution is some kind of direct monitoring. Play through an amp or preamp in parallel or use (probably split) the audio signal after the converter if this is possible. Then you hear the guitar in realtime and this is what you need. Especially if you are playing along a playback track. The recorded notes might be late because of a slow MIDI chain, you can correct them after the recording. If you play live, this is no option of course.
I had this problem and decided do add always a little direct sound and I use hardware for the main sound in most situations. Only the effects are done by the computer and they may be a little late, I don't care about. A short delay can even make your tone fuller.
If you absolutely want to use software, there is no other chance than using the best components you can afford throughout the whole chain and the less CPU-hungry plugins you can get. Good guitar, really fast converter and interface and computer and the "modern way" is almost possible. For me not more than almost.