Oh it doesn't, AMD and Intel gave up on that awhile back. v8086 mode might... but I'd guess it has quite a bit of errata. Everything else has most certainly changed. CPUs don't support the A20 gate for example. Nor do they truly support real mode (they boot in 'unreal mode' now). If you want a 386 compatible you're looking at ALi or DM&P CPUs that are basically Pentium/486/386 clones.
I'd argue the break started with the Pentium Pro, at that point things shifted architecturally.
The 80286 and 80386 never had special support for the "A20 gate". That was provided by (often slow) external circuitry.
Some CPUs (I cannot remember which) built in an A20 gate to their CPUs to improve performance.
The P6 was a complete implementation of the 80286 and 80386, Virtual 8086 mode, TSS, and all - you could boot DOS or an 80286 operating system on a P6 without any problems, although the design was not optimised to improve performance of 16-bit software. This was enough of a problem that they rolled back that design by the Celeron era because there were still a lot of people using 16-bit apps.
I'd argue the break started with the Pentium Pro, at that point things shifted architecturally.