Here are potential issues that may or may not arise from such solution that I see.
Geometry changes. As it has always been, control that the head tube angle of the bike changes in a way that does not worsen its handling. I, for one, use 27.5+ wheels and tires with a fat bike fork made by Surly originally shipped for 26" wheels with 4.8" tires. However, the vendor in this particular case states compatibility with 26", 27.5" and 29" wheels, and so far it was so good.
Clearance issues. Yes, a 27.5+ tire alone would fit; but would all the mud and snow sticking to the tire fit? I've had situations in my life on some bikes when either rear or front wheel got clogged with a mixture of clay, grass, sand and dirt, or sticky snow, to the point the wheel stopped rotating until cleaned.
Tire width variation outside of vendor specs. The actual installed width of a tire depends on the width of the rim used, and it could be wider or narrower than specified. So your 4" can become 3.8" or 4.2" in reality.
For the rest, a trail fork should be as good as a fatbike fork, or even better. For example, RockShox Bluto is considered by some to be "noodly" because its stanchions are just 32 mm and seem to be derived from a cross country fork. So a narrower fork with 34 mm stanchions could be stiffer.