I would like to monitor a set of points from a PLC using the Modbus protocol. I would like to monitor and log Modbus points faster than 1 second. Can I do that with Sinolta?

Yes. There are two steps:
Set up a Modbus scan-interval to your desired frequency (Windows time resolution is about 20 milliseconds so you may not get 1-millisecond accuracy. To be tested).
From point configuration wizard, go to the Data logging tab and enable the data logging feature.
Ensure the Advanced properties are checked. Enable SOE Logging. This feature allows you to log all point changes to the SOE log database as fast as the Modbus can read the values.