I checked out the Halo release week, and the first few months after launch.  It didn't outsell the PS4 any of those weeks, so I doubt it did at any point.  

To be fair though, we never had a 2 month old XBone against a 4.5 year old PS4.

When we look at the Switch's sales potential we have to compare it to the DS and Wii and not to the Wii U and 3DS. When the Switch price was announced I said Nintendo expected it to be a Wii / DS like phenomenon and that's why they priced it at $300: To avoid crazy selling-out situations like with the DS and Wii. 

For those surprised by these numbers: Look at the difference between PS4 and DS / Wii sales. (For some reason the stupid image won't show up in my post preview so you'll probably have to click the link.)

The PS4 has a baseline of around 250k during the year which is really great. But the Wii and DS had baselines of around 400k (!) during their peak years (for the DS that was three successive years, 2007-2009) and both of those systems were supply constrained for a long time. The Switch mimics the DS situation from 2006 (blue line) - see how the baseline fluctuates wildly but goes up throughout the year? That's Nintendo struggling to ramp up production.

Nintendo had a market of 250 million customers back then. Last generations, due to horrible hardware designs (Gamepad, 3D) Nintendo's market shrank to around 80 million customers. But Nintendo's goal with the Switch is not to outsell the 3DS and Wii U combined. It is to get back to those 150m sales the DS enjoyed, maybe even higher. 

Nintendo is now back on track when it comes to hardware and software quality it seems. If they keep this up (and we'll see soon at e3. I still don't trust Nintendo with their software decisions seeing how they willingly threw away their success to make the games they wanted) we will see a few things:

1) The return of evergreen titles: Games like ARMS, Splatoon, Mario Kart, Animal Crossing, etc. will stay in the charts for a long long time (if they are good). Some games from 2007 kept selling well into 2010 during the Wii / DS generation. If Nintendo is smart the same will happen this generation. 

2) Switch demand that far exceeds the PS4: Remember, I'm not saying the Switch will outsell the DS + Wii combined. But it can get to the same level the DS did (again, see those insane 400k+ regular sales?). Nintendo's software and hardware resources will all back up the Switch and the Switch only. Back during the 7th gen Nintendo had to support two systems. Now, it's only one that will get all the games starting 2018.

3) Highly fluctuating sales: The problem with a console backed by evergreen titles is that it's a lot harder to predict demand. Demand can suddenly rise if a new title released but you can't predict if it will go down the week after that. Nintendo had huge supply problems during gen 7 because of this. Sony's baseline on the other hand is more predictable (look at the Wii graph during 2008 - sales went up and down like crazy. Same goes for the DS in Japan durng 2007-2008). 

4) People having no idea what is going on: You will continue to see posts that say "the Switch doesn't have good games" or "I know no people who are interested in the Switch". the Switch targets a different audience that's not represented on gaming message forums. It happened during the Wii / DS days and it will happen again, if Nintendo keeps their good work up. People will simply refuse to believe it and thus won't be willing to analyze it. You can see it now already when people say the success of Bomberman, Tetris, Street FIghter, etc. is due to a lack of games on the system. But the Switch customers (who is really the "Classic Nintendo customer") values games like these more than traditional hardcore gamer games.

You can bet Nintendo is doing everything they can to get Switch production up and running. There is no sane reason to keep production low. "Artificial demand" is bullshit, it's money left on the table. If Nintendo can sell 20m Switch units this fiscal year why would they willingly produce only 10m? It doesn't make any sense. The software is what sells the hardware and Nintendo has a strong line-up with games like Arms, Splatoon and Mario releasing this year. the question is: Will they keep this up? Or will they go back to their Wii U / 3DS days of "we only make the software we want! Here is another Pikmin, gimped Star Fox and Mario 3D Land, haha!" We'll see soon.