Between the grid, a click track and your ear you should be able to work it out if you put some hours in. Chopping audio and using flex time are my two of my most used production techniques.
When editing audio I've gotten into a flow so you can sorta keep feel in the vibe as you line up the track. Like if I were you....
Step 1. Set up some screen set shortcuts to focus on the first 4 bars.
Zoom in so 4 bars just fits in the screen then save this as screen set one
Then zoom into 1 bar and save it as screen set two
Then you can zoom in real close to like 1 beat for the 3rd screen set or whatever you wanna do.
I then map these screen sets to the "1", "2", and "3" keys on my keyboards so I can switch between the views quickly.
Basically the play head works as the point ur zoom will be based on. but if you click on a region that the play head isn't in then logic will zoom to that region instead. that will make sense once u try it and play around with it.
Step 2. Split the vocal into into 4 measures.
With the click track on play the first 4 bars and no doubt it will loop sort of badly (for this tutorial I'm assuming you want to keep the track at roughly the same tempo but tighten it up).
Ill take a moment to remind you of these important keyboard shortcuts:
ESC+1 - Pointer
ESC+5 - Scissor
ESC+9 - Zoom
ESC+E - Marquee (not needed if you change the preferences as i mentioned earlier)
ESC+R - Flex
Turn the click track off and deselect cycle mode to the track does not loop. Now solo the vocal, as it plays count along with it. |1-2-3-4-|1-2-3-4-|1-2-3-4-|1-2-3-4-|
That should give you an idea of where each measure starts and ends. Get the slice tool and slice the vocal into these 4 segments. Line up these 4 segments with the down beat of each bar (the 1).
Note that there might not be a note on the down beat... if you need me to explain this let me know but I'm pretty sure you would already understand that.
Step 3. Chop the vocal into time.
You can start to work on re-alining the vocal so it sits with the click track. Using the marquee tool highlight sections then use pointer tool to move them to where they sit in time with the click track. Be sure to keep listening back to your edits, don't just go by site. Work one measure at a time, you can use that screen set we set up earlier to zoom into one measure, just hit "2" on your keyboard. At this stage ignore the messy tails and overlaps. focus you ear in on the transients of the sounds and getting those in time by chopping arranging the audio. Really trust your ear, some things will sound better here off the grid and don't be afraid to modify the original rhythm and give it your own flavour.
Step 4. Tidy up the tails with Flex time.
After chopping the vocal up, you 4 bar loop may be sounding pretty average still. This is where you can use flex time to tidy up some tails, lengthening and shortening notes to fit with the groove. Uses ESC+R to get the flex tool or you can switch to flex mode but you already know all this as you watched the videos I posted earlier

My usual workflow is to get the tails tight, then listen to how it sits. If you need to add flex markers in the middle of the sound to get things tighter you can get to work on that now. At this stage the vocal should be very tight and flowing how you want it... but there may be some artefacts
Step 5. Attenuating artefacts with automation.
Load up a gain plug in (this is better to automate as it still leaves the fader free to set the overall level of the track). Press "a" to switch to automation mode and draw in fades where needed and ride the levels to mask any unwanted artefacts. You can use the "fades" tool for this but I like automation better, personal preference.
This should clear things up. If your still confused feel free to ask.
As a side note you can use flex as shown in the video's but the quality of using flex in combination with slicing audio yields better results for me and is definitely worthwhile learning. Especially when you get board of just beat making to an acapella and want to expand musically and have some serious fun chopping and re arranging vocals.