I know that they both have a role to play, but could a grammy award winning engineer make a crispy vocal using just his engineering skills regardless of equipment used?
I think the heart of the question is, which is more important: gear or skill?
The answer to that question is skill is more important. Skill is the product of training, practice, and experience, and people with the highest skill levels have a great advantage in producing the best results, in any field.
You specifically asked about the skills of mixing and mastering, but there are two other skills that are more important for quality vocal recordings: singing and recording.
The first and most important step in the quality chain of any music recording is the musician/artist. The skill level of the musician(s) involved in a recording is the number one factor that determines the eventual quality of the recording. Better musicians know how to get the best sounds from their instruments and voices, play in tune and on time, know how to work with microphones to make sure the best sound is picked up by them, and know how to "mix" themselves in with the rest of the band. The skills that better musicians bring to the recording studio make all the other jobs of making recordings easier.
The next and second most important skill in making quality recordings is recording, which might more clearly be called "recording engineering". Once you've got great sound coming from the musicians, you have to capture that sound onto a recording medium. This is a very challenging skill and has a huge impact on the results. Just a few millimeters of movement of a microphone can make a large difference in what that microphone picks up, and can turn an epic drum sound into a dull thud, or a beautiful vocal into a nasal whine.
Microphone selection and placement might be the most important jobs of a recording engineer, but they are not the only tasks that have a great effect on the quality of a recording. The placement of the musician(s) within an air space, the direction that instruments and microphones are facing, the technical aspects of managing the electronic signal produced by microphones, and also any processing done during the recording process are other aspects of recording engineering.
We should also not discount the artistic decisions made along the way. In a big-budget production, there is almost always a person who is an additional artistic expert called a producer who either has the final say or offers an additional opinion on how different playing styles, tones, microphone placement, EQ settings, etc. all work together to create a great work of art. The best producers have skills in both the musical and technical realms, and understand how to make things groove as well as make recordings sound clear and exciting. Their skills are invaluable in creating the best recordings.
The weakest link in the chain will significantly determine the result. A grammy award winning engineer will not be able to fix a bad recording (due to lousy voice or lousy microphoning), like a Photoshop award winning retoucher will not be able to fix a bad photograph (due to skin problems or lousy lighting).
You need to work with solidly good material to arrive at great results.
Yes, any part of the recording chain can be a limiting factor. But the technical level of today's affordable equipment is pretty good. If the performance is good, the room sound is good and the engineer doesn't do anything wrong, premium equipment may not have much to add. When magazines do equipment 'shoot-outs' it's very usual to discover that it's difficult to tell the price of a microphone from a blind test!
From an amateur home recording viewpoint I think you have to have a minimum level of quality equipment or you end up faking it in the mixing/mastering phase with fx. Doesn't have to be very top shelf, but you can't really get good results from the cheapest thing you find at Guitar Center. Of course my voice is hopeless regardless of equipment, but I prefer a pristine warble.
Experience and skill are much more important, the knowledge of the best techniques, how to make the most of any given situation and deal with problems that almost always present themselves, will usually yield better results than the best equipment in the hands of someone who doesn't know how to obtain optimal results from that same equipment. That said, of course you need to go for the best people and the best equipment available to you at any given place or time.