No, we haven't added support for the NADCON 5 files yet. We are actively working on them now. They won't be in ArcGIS Desktop/Server 10.7.1 nor ArcGIS Pro 2.4.
Even when we do support the NADCON 5 files, you will be restricted to 2-step transformation paths. NAD27 to NAD83 2011 will have at least 4 and could have 5 steps depending on whether the area had 1 or 2 HARN re-adjustments.
We do support the GEOCON v1 files but you would still need to do 2 processes. NAD27 to NAD83, NAD83 to HARN could be one then the second set would be HARN to NSRS2007 and NSRS2007 to 2011. Those transformations were added in 10.4.0, but the files are in the separate ArcGIS Coordinate System Data setup. You need to install that separately.
One issue with GEOCON is that it assumes that data was in the most recent HARN re-adjustment for a state. If you're converting from NAD27, our NAD83-HARN conversions use the earlier NADCON which is for the first HARN re-adjustments.
The two step transformation path that is available to me in ArcMap now
is WGS_1984_(ITRF08)_To_NAD_1983_2011 + NAD_19827_To_WGS_1984_79_CONUS
can you add some light to that transformation path?
NAD_19827_To_WGS_1984_79_CONUS uses the NADCON 2.1 NAD27-NAD83 CONUS (contiguous USA) grid file but assumes that NAD83 is equivalent to WGS84.
The WGS_1984_(ITRF08)_To_NAD_1983_2011 transformation comes from the National Geodetic Survey's CORS coordinates page. It converts between NAD83 (2011) and WGS84 at Epoch 2010.0. So you're skipping from NAD83 (1986) about 14 years worth of movement and/or the re-adjustments to HARN, NSRS2007, and 2011. However, the biggest change is from NAD27 to NAD83 and the next was NAD83 to HARN. The latter realizations generally had much less movement than those two.
Disclosure: I am a product engineer at Esri specializing in coordinate reference systems and transformations.