Hey, Michael.  

It sounds like you have a good, methodical approach to learning.  In general, yes it is mostly a matter of time & repetitious practice to make playing more second nature.  But there are a few things that can help your practice more effective.

Responding by point.

"When I have learned a song, most recently, China Grove, You Shook Me All Night Long and Are You Gonna Be My Girl I know when I am actually playing I can’t count my way through it I have to feel it."

That's fine.  It's how most players approach it.  It takes a focused effort just to play the parts correctly in time.  Doing that while at the same time consciously counting beats or rhythms is a extra level.  It does gradually get easier the more you play. 

When I learn a song that's the first step, just play it in time.  In order to teach it I have to make that extra work step to be able to consciously count through it. 

"But sometimes playing arpeggios or just repeating riffs in the song can briefly throw me off as my hands have to play notes in between my foot taps."

That's an indication you don't have those parts firmly under your command.  This is when you isolate a few bars, or enough that you can loop a section in time to repeat them for extra practice.

Sometimes I'll take a one or two bar riff or lick and slow it down to where I can count every subdivision and then play it for 30 minutes (or more!).  The more complex it is sometimes I don't even use the metronome or play it strictly in time until I really get the physical motions to where I can play them with my explicit counting aloud.  I only get the metronome or backing track back out once I can make the playing and count all second nature.

Make sense?

Sometimes for repeated riffs I will make a point of doing isolated practice just counting the riff.  I start with counting each repetition.  Then try to get to 2, then 4, then 8.  Usually the song arrangement can help give you a heads up: the lyrics, a drum fill, a bass line.  But explicit counting at first, outside of playing the song can help.

In the end you don't need to count all the way through a song, or tap your foot all the time.  Those are just helpful tools to help you get to the end goal: playing the music in time and up to tempo.

But when you can count or tap at the same time, then you know you've really got it automated!

"The question is this the right approach and is it just a matter if putting in the time to make if feel more natural?"

In general, yes.  But targeted practice, focused on problem areas is very helpful.

Glad you are enjoying my triads tutorials.  Keep practicing & let me know if you have more questions!