I think you're misunderstanding the purpose of a sound card.
If you have onboard audio on your motherboard, the only reason to get a sound card is if you're an audiophile and just need to have the highest quality audio possible. However, if you're not using headphones costing more than $250, you probably won't notice the difference between onboard audio and a sound card.
A sound card doesn't do anything that the motherboard doesn't do, it just does it better, usually for a hefty price premium.
Most speakers on monitors are not very high quality unless it's an expensive monitor from a reputable company. Having a sound card vs using onboard sound will likely produce no difference when coming out of speakers on a monitor.
Please also note that most monitors that have speakers get their audio through HDMI or another display connector. Not many get them through a dedicated audio connector like a sound card has. Sound cards will usually not connect to monitors.
A sound card does not produce sound on its own either, you still need speakers whether you have a sound card or not.