I guess you can make sure that you're new algorithm isn't terrible at empty maps, but modifying your pathfinder so it does a check to see if it can do a direct walk from the start to the goal, and just returns that straight path would bypass that case entirely.
You're also not going to see any speedup compared to the standard A* algorithm, so you'd mostly just be doing a sanity test to make sure the more complicated algorithm isn't overdoing it.
The most lagging scenario would be when the paths are not straightforward, or when the goal cannot be reached at all. Though the latter, again is a scenario that's best optimized out entirely if possible.