You absolutely can do this. Whether it's appropriate for your situation is a different matter.
Essentially, SIP trunks are like POTS lines or T1/PRI trunks. They are just dial tone. They can be used (and combined) in various ways depending on the business application.
Using that analogy: You could run a individual POTS lines to each desktop (i.e. associate your softphones with raw SIP trunks). This would get you phone service at that desktop / workstation.
If you have more than one desktop, you may want to call between them, transfer calls between them, or have them ring sequential in a hunt group when an inbound call to your company (or a specific department, maybe on an extension) comes in. This is where a PBX needs to exist somewhere.
The PBX can either be on-premise (e.g. Asterisk, Avaya IP Manager, etc.) or off-premise (e.g. hosted by your SIP provider).
Some SIP providers just provide the equivalent of "dialtone" -- just trunks. These can be connected directly to endpoint devices like hardware phones, soft phones, or on-premise PBXes.
Some SIP providers also provide hosted PBX offerings. In these cases the customer doesn't have an on-premise PBX, and their endpoints are configured to point at the provider's PBX.