From a SAIL form page, is there a way to take action within a process model when

Can you please elaborate a bit more when you say take action within a process model ? What type of action are you talking about ?

Once the user has accepted the task, I'm wanting to write to the database and report off it.

You can create a task report for this task. On accepting the task the task owner name and time will be populated in the report.
By Using "Execute Process Report" smart service you can get the task accepted details.

This smart service execution can be configured in your process for every 2 mins whether the task is accepted or not or 10 mins, this depends on your requirement.

Ashley, if thats your requirement and this is only you need to achieve, then you dont need to depend on process model for these operations. You can simply make use of executequery() function within your sail code wherever you want to take the action to perform any SQL related queries and DB operations.
For reporting on that data, you can again make use of the above mentioned function or can even use Query Rules.

Hope it makes sense and helps !