No, the base runs just what I said; in reloading 7.7 Jap, the .30-'06/.308/8mm Mauser shell holder is used. But I will clarify my non-interchangeable statement a bit. The 7.7 semi-rimmed will fit into the 7.7mm rimless chamber but the rim won't fit into the bolt face of the Type 99 rifle. So it won't feed from the magazine, and if it is dropped into the chamber the bolt cannot be closed on it so it can't be fired.
The 7.7 rimless rifle cartridge apparently will feed from the strips, but I have been told that the gun will be unreliable because the extractor won't always grab the smaller rim. I cannot test this condition, as I have no Type 99 HMG handy, so I am going by what I have read.