Yes.
It is not a matter of 'Number of Songs' that is a limiting factor: it is a matter of storage space.
A 4GB mini can hold 3.72GBs of data. Each song file you create has a total size. Song file size is a factor of bit rate and song length. Encode at a higher bit rate and your song file will be bigger. Longer songs are naturally larger in file size.
1,000 songs is just an estimate. Rip mostly songs from the 1950's and 60's (that are shorter) and you can fit more songs in a given HD.
Generally, a 4GB mini will hold around 70 hours of music (if it is ripped in a 128kbps format). How many songs that equates to is a variable based on the length of the songs.