If this happens, IMO, several things follow immediately. Japanese efforts against ROC in southern China are going to be significantly enabled, now able to cross IndoChina without interference. That means the invasion that sparked the U.S. embargos doesn't happen. It also means Britain has to do more about building a Burma Road, or Railway, much sooner.
The other big thing is, it blows up British ops in Africa. Italy is likely still to fold up, but now, there will be Vichy aid from (frex) Syria, rather than German. Just how serious that is for British ops in Africa, IDK, but it doesn't look good. It also likely means a Brit/Commonwealth invasion of Madagascar is mandatory.
No (or less) German involvement in Africa means it's worse for the Sovs, with
X Fliegerkorps available to attack Sov oil (rather than busy bombing Malta). Basing U-boats at (frex) Dakar is a nightmare of Allied convoy escort.
And this is at a time when RN & RCN are already at full stretch...
There's also a chance (maybe not a good one) for Vichy troops in SU...
Does Vichy control of Syria mean German access to Mid East oil is better?
Does the increased "reach" of U-boats encourage more Type IXs being built? Maybe (because they'll be operating farther from home more of the time). Does it mean the Brits will have to shift a/c from Bomber Command to Coastal Command? Maybe--& maybe even to Newfoundland (both a good thing for Britain). Does it make war with Japan less likely? In the near term, at least, yes, IMO it does--& that's good for Britain, too, & not only for the greater number of VLRs available. Does it get bad enough the Brits have to change their approach to bombing Germany? IDK. Does it mean the Brits will need new weapons & equipment to cope with U-boats? Likely--at a minimum, it should see ASV in Coastal Command first (if not kept out of Bomber Command's hands entire).
Does it mean the U.S. never actually enters the war? It might...
Does Germany apparently doing better move Venezuela or Brazil to join the Axis, & provide oil or other supplies?