Hi,
Thank you for contacting us here.
Yes, if you use the CSV-5300H to connect the 3 HDMI displays will work without issues on the DP port. You just need to use the remaining ports HDMI and 2x DVI to connect the other displays to have a total of 6 displays.
If you choose to buy the CSV-5400 you will require to have DP to HDMI adapters to connect to the ASUS VN248H-P, therefore I think this is not the best option for you. If you do, then you can use 4x at 1080p on the MST Hub plus 2 more of your choice from the graphics card outputs.
You will have no problems doing a 6 display setup on the graphics card you have. Please note that I do not have experience on Sapphire graphics card but I am positive they use the reference design as ours.
The Hub will work on Windows based Tablets, on Intel NUC and also any GPU that has a DP 1.2 spec port.

Here are some videos for your reference
DUAL CSV-5300 on a HD 7870. AMD GPU’s have 6 pipelines so if you have DP ports and a MST Hub you can configure up to six displays
CSV-5300 on a R9 290X. This is a similar configuration on your graphics card. I use 2x DVI ports, HDMI and a MST Hub which makes a total of 6 displays.
CSV-5300 with Surface 2. You can use this on tablets as well.
If you have further questions please let me know.