No. With the MMC64 cartridge directly plugged into the cartridge port, it will pull /EXROM low, which automatically makes the C128 boot into 64 mode. Contrary to some belief, this doesn't happen in hardware level, though. The C128 reset routine specifically checks the ROM indication input lines in the expansion port and jumps to GO64 if a signal is present.
As a side note, to anyone who is interested, some further information: on Commodore 128 the /GAME and /EXROM lines are connected to the 8722 and their state can be read at any time from bits 4 and 5, respectively, of the Mode Configuration Register (MMUMCR) at address $D505, in the I/O area ofcoz.
Nevertheless, the reset behavior cannot be changed, because it is done by KERNAL and the code is in the ROM. Well, the soft reset vector is checked first, but there is no way to insert a hook because you will always end up in 64 mode after power-up. So, the short answer without extra hardware is in fact, no.
However, it is possible to add something that will allow resetting into 128 mode, but it involves making a bridge to connect the cart. I am lucky enough to have gotten an expansion port divider that has slots for 4 carts and an individual switch for each of them! I plug in MMC64 or other C64 cart, power on the C128 with its switch off and then turn the switch!
This makes the cartridge invisible at reset time, so thine computer will not enter 64 mode! Enabling it later appears safe and reliable, and at that point pulling /EXROM low matters not (until you reset again). From here on, MMC64 behaves like Retro Replay or any normal C64 cart: the 8 kilobytes of ROM can be seen at $8000-$9FFF in banks 8-11.
Unlike the RR, which was designed to allow resetting into 128 mode, MMC64 has its BIOS enabled by default. You can enter the monitor and start hacking:
D88009
The registers are available in in the I/O block at their regular address:
>FDF10
Disabling the cart (by setting bit 7 of $DF11) had no effect in 128 mode. I am unfamiliar with RR-Net and I couldn't get it to show, however. Also, the WarpCopy server crashed immediately when I started it from the memory card (in 64 mode).
I hope this information is useful to someone.
PS. When I was testing this, I found that the value of 6 that you get from the status register ($DF12) with a card in, changes to $1E when you take the card out, ie. additionally to the card indication bit, the write enabled bit also toggles depending on whether a card in inserted.