Asterisk is usually hooked up directly to a T1 circuit. I guess one can place a router at the Telco Demarc then pluck the number of voice channels off the 24 channels (assuming a full T1) into a separate T1 card on the router which provides telephony services.
Many times people have existing PBX systems (Avaya, Lucent, etcā¦) and they attach Asterisk on it to provide extra services: queuing, better call routing, etc⦠In this case, people would just pipe the T1 into the existing PBX, then over a channel bank or FXO/FXS cards like the TDM400 (maybe ethernet depending on how new the existing PBX is - using H.323/SIP) into the asterisk.
But this does nothing to solve the problem with modemsā¦
Typically modems are kept to separate lines that are not doing dual service as a voice line as well. The exception here are FAX lines because of the way Fax machines identify themselves over the phone. If youāve ever had a fax machine call you, you hear the remote end beeping. Thatās telling the local end that itās a fax machine and should go into fax negotiation modeā¦
Analog modems donāt do this. Reason is that the typical handshake is that the answering modem sends the negotiation tones and the remote end answers them. Just think about them poor souls that inherited BBS or Tymnet/Telenet telephone numbers that no longer are in service 
Asterisk may or may not work as is. It depends on many factors including transcoding of codecs, latency and aurial bandwidth. Iāve only presented my experience and study on the subject. (See also FreeSwitch which details out technical shortcomings in Asterisk)
However, what I did want to point out was that there are other products that market this capability (ie: Cisco). Personally, if it were done, and even a software modem were created out of it to connect to analog modems, it would go a long ways towards bridging the digital divide we opened by going to broadband. The standards are there. It can be done and should be written to continue making the product (asterisk/digium) a better product.
Since most people donāt have access to modem banks or remote dialup nodes, many services that could be āfakedā with serial to ethernet adapters will never come to fruition because there is a PSTN world that these devices cannot accomidate for.
And all of this at the turning point in history when Long Distance calling doesnāt require bank loans, prostitution of your spouse, selling blood and plasma just to pay your bell company telephone bill. Iām not too old to remember the break up of bell (vaguely) some 25+ years ago or the myraid of services like CompuServe/Genie or PCPursuit (15ish years ago).
But as history would have it⦠Bell is back as one piece⦠just the market is still deregulated⦠too funnyā¦