unfortunately, there's no real 'hard and fast' rules on this. For instance, arm-none-linux-gnueabi-gcc doesn't specify if it is for armv9t or armv5tel or what. Deducing which capabilities a cross compiler has from it's name alone will be a very difficult and error-prone process.
However, generally, the bsp authors/support staff know what the specific board has been qualified for and so distribute a proper cross compiler. If you're worried that it won't properly build your kernel - you could be right! The linux kernel team has a tendancy to use undocumented and potentially 'buggy' side effects of the gnu compilers which end up tying the kernel to a specific gnu compiler version (and sometimes even weirder options requirements). This has generally become less of a problem in the last few years, but was REALLY bad around 2001-2003. Enough of the off-topic though.
The only way to know if the cross-compiler you have will do what you need it to do, sadly, is to use it and discover issues when they crop up. Sadly, this is one area of the open-source realm where most of the information involves a heavy amount of voodoo and waving dead chickens. Google will be helpful, but only if you're willing to spend a week wading through every email thread in the first 50 pages of results.