Here is the thing to keep in mind with splices of all types.
The goal is to have a nice and smooth transition in all stages of the rope, the throat, the core taper, the jacket taper (in double braid), all need to have a nice smooth transition in order to provide the highest level of strength.
In terms of our discussion here, with the hollow braid rope like Ice tail (or tenex, tech cord, etc) the primary emphasis will be on having a nice taper, which will provide the maximum strength and holding power since the stresses on the rope will be evenly distributed along the longitude of the rope.
Having a whipped portion within the rope could possibly deter from this goal if that portion of the splice is not tapered and is simply cut and whipped. On top of that, from a usability standpoint, it might hinder a good knot from being set on the rope.
Anyway, method of whipping the core rope will probably result in a rope that will hold you, and eventually you will probably retire the rope due to it being worn out rather than failure.
If you got a brummel splice in there, I wouldn't worry about the security of the splice. Once you load that thing, they tend to set and actually become tough to take apart. Using some extra Ice tail fibers to stitch up the brummel area will keep it from coming apart in a no load situation.
Even with our splices, if splice something like double braid nylon and do the final bury, it really is tough if take the splice apart. Once it gets a good weight load, it becomes darn near impossible!
