Ingram's utilization has increased weekly (11>13>18>22) and he played on a season high 62% snaps in week 4. Payton is going to use Ingram, yes.
I think Ingram's skillset more closely resembles AP, so the logical leap is to think AP leaving opens up the door for more usage from Ingram, and Kamara will stay the same or only a slight uptick. I think that is logical reasoning looking at past performance.
However, I also think Peyton has desired a back with Kamara type skillset (Kamara is great catching passes, but unlike Reggie Bush, Kamara can also run between the tackles effectively as displayed in college). C.J. Spiller was a failed attempt to fill the role of a versatile back that can be effective in the run & pass game. There is no doubt Peyton has been searching for this perfect fit back since the Deuce McCallister/ Bush days. Peyton has never truly had a back with the complete skillset (Sproles comes closest but his size did not allow him to be full time), and I know his style of offense greatly values a RB with such a skillset. In fact, he has played sub par players (Cadet/Pierre Thomas, etc.) to Ingram's overall rushing talent because they are better than him in the passing game. Kamara is no slouch at running the ball, and for those thinking he can't carry the load, he's one inch taller than Ingram, but weighs the same. This isn't a scat back, or cop only type back.
The bye week is usually the week teams make adjustments to their game plan and historically we see rookie upticks in usage. AP being traded helps to fund this idea of making wholesale changes in strategy. It is conceivable that both Ingram and Kamara see upticks in usage, or one greater than the other, but when we factor in Peyton who used Sproles so effectively in spite of him not having Kamara's size, one can see the value in having personnel on the field that does not tip the hand on the play call to be run or pass. Kamara has a huge edge here over Ingram in versatility and unpredictability, and Sean Peyton more than any other coach values this in his play calling. We are talking about a coach who was trailing 10-6 at halftime and onside kicks the ball in the super bowl to start the 2nd half. You think he values unpredictable play calling? I think AP was forced on him and he absolutely loathes putting in a guy that was so one dimensional (and is glad he wasn't effective). Where as a different style coach like Fox would love to pound the rock 20-30 times with AP and feel totally comfortable doing so, Peyton felt put in a box running AP out to the huddle.
Another way to look at this is Kamara gets all the AP snaps and Peyton gets to put in totally different play packages which he is comfortable running for those 8-9 carries AP would have got, but we will not truly know until after we see 2 or 3 games coming out of the bye.
If you recall, the saints were not expecting to get Reggie Bush, it was a surprise and once they got him they changed the entire game plan to suit his style. I would say the Kamara's skillset is even better suited to Peyton's ideal back as he can also run effectively between the tackles even if not quite as fast or dynamic as Bush in space, he is still above average there.
This is an older article, but confirms a few of my thoughts.
http://www.theadvocate.com/new_orleans/sports/saints/article_2b820100-31aa-11e7-8da3-8ff58a2647f6.html
I've went after Kamarar everywhere I could. BUT--I do have one team with both Kamara and Ingram. The million dollar question is--who do you start if you ha e both assuming you already have another #1 like Frreman, Gurley, Bell, etc...?
We don't know, but I would bet on Kamara as the ideal back suited to Peyton's ideal style of play. Anybody who has watched Ingram's usage over the years has either scratched their head about his usage or lack thereof, or the merely understood that is not the type of back Peyton likes to use in his style of play calling. As the rookie matures, I believe Peyton would have him in the game as often as at all possible. just imho