My stock CD32 doesn't have any connectivity that would support a browser. Adding an SX-1 module would make the unit a lot like an Amiga 1200 in a silly case w/ a CD-ROM drive, but you'd be limited to serial connectivity and SLIP/PPP (since there's no PCMCIA slot-- the typical method of adding Ethernet connectivity to an A1200).

I didn't have a CDTV so I can't comment on the hardware specifics. If I remember right it's an Amiga 500 (or 500+?) in a funny case w/ a CD-ROM and would suffer from the same lack of connectivity as the CD32.