Ian,
Yes you would be covered. But for clarification, "Up to the Minute" would not affect your current logs and your ability to use them for restore from the most recent backup, either way.
Consider our previous A, B, and C scenario: "Up to the minute" gives you the ability to have a retention (for example) of three nights' FULL backups and always have the transaction logs on hand to restore up to the minute for any time after A up to the current backup time--including any time in between, even if... (here's the difference) you *remove* the Full Backup "B". Because you will still have retained all of the logs that were written after A, and after B, and any that have happened since C, you will have all of the database transactions for the whole duration. If you removed Fulls B & C, and wanted to restore up to the minute, you would still have the baseline Full A to recover, then all of the logs to enable you to play back to the time of the most recent snapshot (full or incremental).
One more fyi, once Full A expires, all the logs between A and B would expire from the SnapInfo directory. Then you would have B, C, & D's logs. Once B expires, all logs between B and C drop off, and so on...
I hope this helping...