To answer your question whether you’ll hear and improvement depends on how good your sound card is, some are very good but more often than not the standard ones on cheaper laptops won’t be much cop and can be bettered with an off board DAC. You can take digital signal out via USB and also double check the headphone out socket as these often run a optical signal in parallel, if that is the case you may well see a red light if you take a look.
I’d say plus one for the Fiio also have a look at this, dirt cheap but has many fans: There is also an emerging breed of micro USB dacs such as the Dragonfly
Annoying, can’t see the verification box to post links but this is off ebay - Digital Optical Coax Coaxial Toslink to Analog RCA Audio Converter Adapter w/Opt seller xingye 1029