No, not really. You don't want to run the stock cooler if you can afford to avoid doing that. The stock coolers are VERY problematic. What happens is that at least with a decent aftermarket cooler you extend the peak boost frequency and duration in most cases over what you get with the stock cooler, because the stock coolers are not very capable.
Also, the stock coolers tend to be VERY annoying, and every single one I've installed on any Ryzen platform has had terribly annoying cyclic up and down fan behavior that drove me and the customer completely nuts no matter how I configured the CPU cooler header fan curve or thermal points and regardless of how good the case cooling itself was. There is only one reason to stick with the stock cooler and that's if you have no other choice because you can't afford anything better.
I'd recommend this cooler over that Noctua cooler, unless you have your heart set on Noctua (in which case I'd either go for the Noctua NH-U14S or the NH-U12A) because it outperforms the NH-U12S, looks better and is less expensive. I've used this on a number of Ryzen 3600, 3600x and 3700x builds and it has done a very admirable job for a less than 50 dollar cooler. Thermalright has been at this longer than almost anybody else in the industry, and makes very high quality cooling products much like Noctua. If you buy the RIGHT product, I'd put Noctua just slightly higher in terms of quality and performance (Mostly better noise levels from superior fans) though.
PCPartPicker Part List
CPU Cooler: Thermalright TRUE Spirit 140 Direct 73.6 CFM CPU Cooler ($42.99 @ Amazon)
Total: $42.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-12-23 13:13 EST-0500
If you can afford the NH-U14S or U12A those are good choices too for this CPU. Actually, any of these are a good choice, from highest performance (top) to least performance (bottom) on the list.
Noctua NH-D14 (Replace stock fans with NF-A14 industrialPPC 2000rpm)
Noctua NH-D15/D15 SE-AM4
Noctua NH-D14 (With original fans)
Thermalright Silver arrow IB-E Extreme
Cryorig R1 Ultimate or Universal
Be Quiet Dark rock Pro 4
Thermalright Legrand Macho RT
Phanteks PH-TC14PE (BK,BL, OR or RD)
Deepcool Assassin III
Thermalright Macho X2
Thermalright Macho rev. C
Thermalright Macho rev.B
Thermalright ARO-M14G (Ryzen only)
SilentiumPC Fortis 3 HE1425
Thermalright Macho direct
Deepcool Assassin II
Noctua NH-U14S
Thermalright true spirit 140 Direct
Cryorig H5
FSP Windale 6
Scythe Ninja 5
Scythe Mugen max
Scythe Mugen 5 rev.B
BeQuiet dark rock (3 or 4)
Thermalright Macho SBM
Noctua NH-U12S
It may not be obvious, but is probably worth mentioning, that not all cooler models will fit all CPU sockets as aftermarket coolers generally require an adapter intended for use with that socket. Some coolers that fit an AMD platform might not fit a later AMD platform, or an Intel platform. Often these coolers come with adapters for multiple types of platforms but be sure to verify that a specific cooler WILL work with your platform before purchasing one and finding out later that it will not.