Dialup is still very prominent in certain areas of the United States and many other parts of the world (though nearly nonexistant in others still). But enough about that.
Dialup and broadband work on a very different system, and won't work that way, though both use the TCP/IP method for communicating when connected to the internet. What dialup mainly differs in is how it connects. It works on the assumption that there is a dial tone, and using different DTMF tones, one can reach a destination (ISP) and begin transferring data converted to audio over the phone line. It's an offshoot of the days of very old modems that actually worked with a real phone held up to a speaker. No communication will be made until the modem recognizes that it has connected to a remote machine accepting connections.
Ethernet (Broadband) works on the assumption that the connection is direct, and that any actual physical negotiation to the ISP is done by a different device (eg. cable modem, dsl modem, etc). It simply transmits electrical pulses over eight copper wires at a rate of upwards to 100mbps (Cat-5E). Newer Cat-7 cables can support over 10gbps, given that the devices connected by the cable also support it (otherwise, the lowest speed is used).
These both use different drivers to work properly, and thus a dialup modem will never be capable of connecting to broadband. Furthermore, the first device you've shown looks to me like a USB modem, which will definitely not support what you're trying to do (since it's a modem, itself), and the same goes for the ethernet device. This added to the fact that they both draw power from the USB bus, and thus won't be powered in the first place if used in this configuration. If it were possible to get these devices to work in the way you want them to work, the differences in the wiring layouts would mean you'd have a lot of issues with actually getting data to transport correctly.
In order to set a Dreamcast up to broadband without a BBA, you would need to connect it directly to a PC using a phone cable (assuming the PC has a modem). With a little fudging around (I haven't done it), you can make your PC listen for dialup connections, and once the Dreamcast makes the connection, you can use the broadband set up for that PC. This is much more complicated than it seems, and I've read that it takes a lot of trial and error to even get the Dreamcast to accept having no dialtone and just use the null modem. However, if you do get it working, you will still be limited to 56k speeds, since that is all that a standard modem (and traditional audio-based communications) can transmit/receive. I have no idea if this can be used to do development.
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