Isn't the answer always, "It depends?"
Your analog modem can only attach directly to the digital telephone network through an analog telephone line. For certain telephone systems, analog adapters are made that allow you to plug your modem into the adapter, which plugs into the ISDN or proprietary digital telephone line.
The fact that you are using a cable that is RJ-45 to RJ-11 indicates that what you are attempting to do probably will not work. Analog telephone lines are RARELY put on RJ-45 outlets. However digital telephone lines are frequently put on both.
A simple way to determine if your modem will work on the phone line is to turn the telephone over. If it has a REN or Ringer Equivalency Number, then your modem should work. If it does not, then the modem should not work (US of course).
I've heard the urban legend about digital lines destroying analog modems, but have never seen that happen. There is no voltage difference in any of the telephone systems registered with the FCC for use in the US. That is because it is a National Electric Code requirement that the telephone instruments use "low-voltage" which translates to less than 50 volts. That is why the battery plant in a telephone system is -48 volt, just within tolerance. Of course there is compensation for voltage drop, and most battery plants actually operate at -54 VDC.
There may be a current difference for digital instruments, but I haven't seen that either. Most operate at 40mA or less, just like their analog counterparts.
And considering that Ring voltage is frequently in excess of 200 VAC (20-30 Hz) and the modems handle this without an issue, it seems highly suspect that the modems would have a problem.
All of that said, there is a company called Konexx who make an acoustic adapter (fits over the handset) with which I have achieved rates of up to 14.4K. They also make a handset cord adapter that I have used to achieve rates up to 28.8K. You will never achieve rates over 33.6K with these types of devices, but they are functional with every make and model of digital instrument I have ever tried them with. A definite must for the road warrior.
I found the handset cord adapter at:
Good luck!
pansophic