You can - the Wi-Fi gate outputs are connected in parallel to the wall switch - the gate must have at least 2 outputs (these blinds are controlled by directional buttons - there is no single step by step input, you can also use 2 gates with single outputs).
Just check (neon indicator) that the control signal on the button is not a 230V case - then you have to use a gate with 220 outputs or use intermediate relays.
As for the gate - very company solutions (e.g. Hormann or companies from the range of alarm technology) are also very expensive.
But there are equipment from the border of DIY - e.g. Electrodragon (for gouges) or Sonoff (ready solution with access via a cloud from an external net) for less than PLN 40 a piece.
If you have a lot of blinds and want to control them independently - then you could consider equipment from a simple smart home circle but you need to analyze the costs - Vera Edge from Hong Kong, Croatian Zipato Zipamini (switchboards for around PLN 500 for the simple version) or Polish Fibaro HCL (ok PLN 1,000 for the simple version). Prices of executive modules are unfortunately large (Z-Wave radio system) - from PLN 140 for the cheapest single-channel.
If you have the option of releasing cables and you care about internet control - there is still a Polish SterBox (about PLN 500 for a drug).
