I'd expect that everything will work from a technical point of view but the big problem, as you alluded to, is the delay that this will introduce and the impact of that against personalisation activities that change page content. GTM can only be loaded asynchronously, so even loading Target directly via GTM ends up with flicker between default & variant content; so if GTM loads Tags which loads Target that flicker is going to be even worse.
I don't think Adobe have any documentation on the topic but it's well established as bad practice to even be running more than 1 tag manager, let alone having 1 tag manager load another. There should be no good reason to run two tag managers - if Target should be loaded via the tag manager then you can't use GTM due to lack of sync loading functionality, and therefore Tags would be a better option; however, if GTM is the preferred tag manager then the best option would be to load the Target/Web SDK script in the <head> of the page so that personalisation use cases can be delivered without flicker
