The answer is no. Faster internet speed does not increase wifi range. Let us understand with the following scenario.
Assuming that you have a wifi router at home or office and planning to upgrade your internet plan with a faster speed. The internet speed is what your ISP allocates for your internet and not your wifi.
Your wifi range is dependent on the type of the wireless router you have. Your range will not increase if your internet speed is upgraded.
So you should not do the mistake of upgrading the internet for increasing your wifi range.
The following are the three options you can use to increase the wifi range.
1. Long range wireless router
You can upgrade your router with a wireless router with long range. Long range wireless routers would increase the wifi range. The wireless router can be purchased based on your coverage area requirements.
For example , the TP-Link AX5400 WiFi 6 Router (Archer AX73) is good option for a long range router.
2. Wifi extender
If you want to keep your router , you could either use a wifi extender or a powerline adapter. These devices would also help extend the wifi range .
Wifi extenders connect to the wireless router using the wifi link. The NETGEAR WiFi Mesh Range Extender provides a coverage area of 2300 Sqft.
Wireless access points
You can also extend the wifi range using wireless access points. But for this, there should be ethernet connectivity between the wireless router and the access point. Access points can be purchased based on the range your require and the number of connections.
For example, the NETGEAR Cloud Managed Wireless Access Point provides coverage for an area of 2750 sqft and supports 256 devices.
It can be observed that by upgrading the internet speed, your wifi range would not increase. Based on your requirements you can use any of the three options mentioned above. The best option for a basic home or office would be to upgrade your wireless router with a long range router.