Certainly...
Exactly what it says on the tin. Let's butterfly C.F Smith's fatal accident. Would Sherman be able to rise as he did OTL with the presence of a surviving C.F Smith?
For those that don't know who C.F Smith is:
https://en.m.wikipedia.org/wiki/Charles_Ferguson_Smith
Certainly...
In terms of general officers in the western theaters, the initial (1861) call for 500,000 long-service USVs, and the increase in the regular establishment approved in 1861 yielded a total federal force of ~525,000 by the spring of 1862; this was the equivalent (roughly) of some 48 divisions using McClellan's organization for the Army of the Potomac's divisions (hq, three brigades of four regiments each, divisional artillery) in the winter of 1861-62, with remainder made up of corps, army, department/theater, and administrative elements (including cavalry divisions/brigades, corps and army artillery, engineers, garrisons, etc).
This is the equivalent (again, roughly) of sixteen corps equivalents (call it three divisions each); of those, roughly nine corps equivalents were organized east of the Appalachians and roughly seven west of the mountains, for a total of 27 and 21 division equivalents, respectively.
Of the 21 in the "west," the equivalent of nine were raised in what (by the middle of 1862) was Buell's department, six in Grant's department, and six (more or less) in Halleck's command west of the Mississippi.
This suggests -again, roughly - three armies and nine corps, which suggests the following:
West of the Mississippi - Halleck, with Pope and Curtiss as commanders of corps equivalents;
East of the Mississppi/western Tennessee - Grant, with (presumably) CF Smith and Sherman as corps commanders;
Central/eastern Tennessee - Buell, with Thomas, McCook, and Crittenden as corps commanders.
Depending on events, Rosecrans and AJ Smith are both potential alternates for some of the above.
The point is that given the size of the US forces by 1862, east and west of the Appalachians, there was enough "potential" scope for both CF Smith and WT Sherman to rise to corps/army/department/theater command...
On edit: note the numbers above do not include enrolled state militia (federal funding); state troops and milita on active duty; various local auxiliaries; or the Navy, Marines, Revenue Service, etc.
Best,
