Yes, if properly connected and it also depends on how secure you VPN is, if you use a free VPN then it might leak your activity logs and other detais. Know more about how VPN works for Anonymity using high-level encryption: Virtual Private Network (VPN) uses mix of various technologies like dedicated connection and encryption protocols to create virtual Point-to-point connections and connects you to the internet through an encrypted tunnel and transmits all your internet data through this tunnel and the data transmitter is so secure that even if intercepted, the snooper cannot read the data because of the encryption. This way VPNs can provide you security and anonymity over the internet which is required when you are torrenting or using P2P file sharing platforms etc. or to avoid hacking, spamming, snooping by the government and surveillance agencies and other cyber attacks. VPNs also let you change your geographical location without being physically moving to any other country you can show the internet you are in that country, how? The answer is simple, VPN alters your IP address and let you choose any country’s server provided by it and changes your IP address to that country’s IP address. This way you can access all the blocked websites of any country you wish to, so you may live in UAE, but internet displays you are in New York city, magic? No, the technology of a VPN. So what you need to do to use a VPN for all the aforementioned reasons, first you need to decide why you want to use a VPN? For which device, you want to use VPN? Then once you know the answers, choose the right VPN according to your purpose, device etc. and it is not difficult at all. For instance, you want to access any streaming channel blocked in your country, so you need a VPN. Select a VPN that is best for this purpose by searching your query on Google, get a little research, read some VPN reviews. see these secure VPNs for Anonymous connection; ExpressVPN NordVPN
To add to the other great comments here, your web activity will only be hidden if that traffic flows across the VPN. In a typical VPN from, lets say, a computer at home to a corporate network, the VPN may only be configured to route traffic to the corporate network through the VPN tunnel.
All other traffic would be routed normally, and be visible to the local router.
This is known as "Split Tunnel" and is generally configured at the VPN device the computer is connecting to.
A quick way to check would be to compare your public IP address when connected to the VPN, to when not connected (such as from What Is My IP – The IP Address Experts Since 1999). If they are different, then your web traffic is flowing through the VPN, and you are using the corporate office’s internet connection.
Use some secure affordab;e VPN like CyberGhostVPN