Yes you can download songs from limewire using a dial up connection. I use to do it back 5 years ago. But I can definitely assure you that it will take you a long time just to download a single song. It might even save you money just buying the song from Music store.
usually when download off there , it depends how many people have that file. if 100 people have song A then it is going to download much faster than song B with only 10 people. download depends what connection you have. if you search a song using limewire, song are the top end of the list usually will have more people.
Yes as long as you have an access to the internet you can. But the problem is it suggests time. If the approximate download time for one song is about 3 to 5 minutes on a DSL/ T1/ Broadband. By using Dial up maybe it will take half an hour or beyond.