I do use cash upgrades quite frequently. My main employer (the state) only pays cheap economy-fares.
On the other hand the Agents at the SEN or HON Hotline often have really no clue about the rule and the systems. Sorry, this is a sad fact. In most cases I know the rules better than the agents. Sometimes calling the supervisor may help (they have more clue but are far from good).
Advance payed cash upgrades and auction upgrades do result a milage value for business class. It is sometimes quite a lottery, in which fare bucket you will end. Auction Upgrades end mostly in P or A. For P it can result in lower milage values (but HON-Miles).
Upgrades during Checkin, at the airport, or on board have no extra miles.
Cash upgrades tend to mess up whole bookings. On multi-sement-flights the upgrade of one segment did block the upgrade chances on all of the other segments. I had that a few times, and the call center agents did not have any chance to solve it (the booking class for the cash upgrade is not available: Which was ........ at that time).
What stays: Checked luggage allowance, and all the other T&C of your original fare.
If you rebook, you get a refund for the cash upgrade.
Since some time you will still have the original Cabin Class on your Boarding-Pass. That is not a bug, but a feature (Many Call-Cente Agents: That is done on purpose). Besides from the "waving a C/F Boarding Pass to the plebs" that may have few issues:
- Fast track at some airports. You are eligible as part of the rules but some Staff does not know that LH issues Business Class boarding passes that show "Economy"
- The Hand-Luggage-Stasi: "Oh you are traveling in Economy and have to check in your hand luggage"
Been there, done that.
- Lounge-Access
The rules are quite clear on the webite:
https://www.lufthansa.com/us/en/upgrade-options
I did complain quite a few times, but got as a response: "This is done on purpose". "You have a Status anyway".
On my Short flights the free middle seat an the extra hand luggage are the main features for the upgrade.
Sometimes the seat-number helps (Sitting in 1A). The Barcode shows "Class-C" so the computer says yes in those cases.