Speed of data gleaning from 3 IC2 Sensors

I am wanting to build out an Arduino Due to control three MS5803 sensors. They interface either with I2C or SPI. I am wondering if I would be able to sample every 1 ms and move the data to my computer, or if not, what frequency I would be able to sample at. Ideally I would like to be able to sample data over about 5 min. I am trying to decide if I want to invest in 3 sensors to start or fewer and maybe add more later.

To break it down:
Can I run three I2C easily on the Due?
How quickly can the Due talk to all three and send data?
Is it possible to read and time stamp the sensors in parallel (I realize that it would have to be divided in time technically because it is only using one processor. The question is more what is the cost in time of timestamping all the data)? Or is there another way to accomplish syncing the data?

I'd suggest to use SPI instead of I2C, because the sensors lack programmable I2C addresses.

Since the conversion time of the sensor is 1 ms minimal, it may be hard to obtain samples at that rate, including transfer times and other activities (interrupts...) on your system.

Measurement synchronization is not a real problem. The commands for starting a conversion are sent quickly, so that the conversions start at almost the same time. Then you have to wait for the end of the conversions, with much time left for computations, timestamping and more.