It would yes. If you want to record separate tracks at the same time, you're going to need an interface with at least four inputs. Someone will come along soon and suggest something.
Something like the Focusrite 6i6, which has two mic/instrument inputs (1 and 2), and two line inputs (3 and 4).
So... you could plug your vocal mic into input 1, your guitar into input 2, your bass through a preamp or a pedal or something into input 3, and your synth into input 4.
Or swap the bass and guitar round. Or send the mic through a preamp/channel strip/something that outputs to line level, and use the instrument inputs 1 and 2 for guitar and bass.
A Behringer BDi21 is very cheap and quite loud (in a good way) on its line output, so that would work: vox 1, guitar 2, bass 3, synth 4.