To address your direct question, whether or not a service can detect that you are reaching it with a VPN service in the middle, the answer is a soft maybe. There are several heuristic methods, but they will not be entirely reliable and using them will risk false positives. Most service operators probably wouldn't go beyond filtering of known VPN services, which is of course widely implemented.
One reliable method is active probing of the traffic source, which is sometimes done, but it comes with some hazards for the service operator and is often easy to defeat.
OpenVPN traffic, even encrypted, can look unique enough somewhere in the 'stream' (to borrow the IDS/IPS term) to be reliably idenitfied.
I'm talking about the part of the connection outgoing from the VPN, not the incoming traffic to the VPN, to be clear. I know for example that China can do deep packet inspection and that there are a number of projects to attempt to thwart this technique. But you seem to be saying that the part after the VPN can be identified?
I'm talking about the part of the connection outgoing from the VPN
your understanding is correct—that the 'segment' between VPN server and final destination/employer's public-facing infrastucture is no longer traversing a VPN tunnel and therefore could not be fingerprinted as VPN traffic.if using a public VPN service provider, it would be identified, however (quite easily and at very low technical cost mind you), based on source address, as public VPN service provider netblocks are well-documented.
see, for example: https://github.com/X4BNet/lists_vpn (first search engine result for me querying "vpn ip list")