There is no published info on how BA decides to Op-Up any pax but the common belief is that BA (like any other airline) will upgrade its members first then OW ranks...so in theory you would have better chances with BA silver than OW Emerald.

In terms of other benefits, not really if you are already OW Emerald. There are some points that you may wish to consider if you are talking about BA Gold (Silver not so much)...

-use of double Avios if you are avios rich and there is no availability to get a seat or two

-to complete party (or something like that) when you have another person flying on a separate PNR and wish to join the two together for seat selection, etc.. (I don't believe this is a OW benefit and is exclusive to BA Gold members, but others may correct me)

-additional reward seats made available in Economy for BA Golds (again, think this is exclusive to BA Golds and not extended to OW Emeralds but might be wrong)

-no fees (supposedly) if you cancel a booking as a Gold (again, don't imagine this is a OW Benefit?)

-IRROPS (likely BA would do a bit more for you quicker than for a member of the alliance, YMMV)

-status matching? (in case this is of use...Might be of use to have BA Gold or Silver compared to AY for any future status matching programs...

But in general no. If the above are true then maybe depending on your situation and how much bother it would be.

HTH.