Out of curiosity I called this resort Ban Sainai and checked on their wifi they told me they have wifi signal throughout the resort not just the rooms and reception area and that its high speed with strong signal throughout. Happy holiday Leongsam.
As a backup bring along a mobile hotspot, modem dongle or a phone that functions as a hotspot. You can buy SIMs at any 7-11 that are provisioned for data for 300B or less for a week and get roughly 4-5Mbps down (in a city area, not sure about Krabi). The one thing that I've learned is never take what a hotel says at face value especially with wifi.
The Thai culture is one that wants to please and they would never say anything outright that something is negative.
More likely than not, based on the photos alone, this is a nice hotel and nice hotels usually have fast internet.
