Push your budget up to around £300 and the answer is, yes, it probably will sound better.
How good a external Sound Card in the £50 to £100 range will sound is debatable.
There is a Behringer USB audio interface that is very low cost, about £35; though I can't remember the model number. A few members have this device and are pleased with it. But I can't personally say with any certainty that will will sound better than a direct wire connect.
Found it -
Behringer UCA202 USB Soundcard - Google Search
Depending on where you are, the
Audio Streamer II Asynchronous USB DAC can be had for about US$160
https://www.google.com/search?hl=en&....0.OX3mbczXuUk
I know Audioengine makes a USB DAC, let's see if I can find something on it -
Audioengine D1 Audioengine D1 - Google Search https://www.google.com/search?hl=en&....0.YPo7TYI8zGM
Audioengine is a company founded by a couple of engineers who previously worked for APPLE.
Perhaps others will have other recommendation for an External USB DAC
Steve/bluewizard