You can use it as a 16kB RAM expansion at least. And with some programming you can use more... 
Now that I mentioned it.. the box also said you could, so perhaps the manual tells us how?
@RetroTechie never returned my Rom Hunter mkII neither did he do anything about it, so I obtained another copy that came with manual and disks. Indeed, the manual was helpful. It indicated that I had to use "filers" in the bundled disk. That disk contained much more than the one I previously had. It contained the "filers", the mapper fixes for Cross Blaim/Harry Fox Yuki no Maou Hen/Super Lode Runner/Xanadu/Shalom/War of the Dead/Game Master 2/Bouken Roman/Hydlide 2/Pennant Race. I dumped GM2 and though it differs from the ones online, it's playable.
The manual doesn't state anything about Rom Hunter mkII's structure but pages 8-9
describe the usage of Rom Hunter mkII's RAM. I hope its translation below opens your insight;
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To use ROM HUNTER as an expansion RAM
You can switch 16 KB between memory addresses 8000H-0BFFFH (page 2) to 16 banks of 0-0FH and use it.
7000H
Bank switching register
It is a write only register so the value read from there does not match the written value.
0000 page 0 4000 ROM HUNTER OS page 1 8000 page 2 Bank 0-0FH (16 bank_) C000 page 3 FFFF
Write a value of the bank you want to select to address 7000H of ROM HUNTER MKII then the bank of 8000H-0BFFFH of the memory is switched.
If MSX has chosen a RAM within ROM hunter as the SYSTEM RAM area and a BASIC program or such is present there, switching the bank causes the BASIC program to be modified to a different program so be careful.
A simple program to switch the bank is shown in the next section.
This program is relocatable therefore operates from an arbitrary address in the memory RAM.
For example, if you have entered it from 0D000H address, the start address becomes 0D000H and if you have entered it from 0C000H, the star address becomes 0C000H.
To use it, load the value of the bank (0-0FH) to accumulator A then call the start address of the program, then the bank is switched.
(Bank 0 is selected at the point of the power startup.)
0D000: F5 AF 4F 06 00 21 C1 FC :A7 0D008: 09 7E E6 80 B1 F5 21 12 :9E 0D010: 50 CD 0C 00 FE 59 20 14 :94 0D018: 23 F1 F5 CD 0C 00 FE 4F :17 0D020: 20 0A F1 D1 5A 26 70 CD :99 0D028: 14 00 FB C9 F1 CB 7F 28 :33 0D030: 06 C6 04 CB 67 28 D6 E6: E6 0D038: 03 3C FE 04 38 C4 F1 FB :31 0D040: C9 00 00 00 00 00 00 00 :D9 : : LD A, 01H 8000-0BFFFH is CALL 0D000H switched to bank 1. : :