League of Legends (LoL) Question: AP Kog'maw in solo Q?

It depends solely on how good at him you are.

Kog'Maw is a very fragile champion with almost no cc, which means that he have to rely on his teamates to protect him in some situations. Considering the lack of coordination of players in solo queue and the popularity of hard engagements, it is correct to affirm that Kog'Maw is disavantaged. I recommand you to pick him when you have a poke composition and when the enemies doesn't have any form of lockdowns.

Well AP Kog Maw in Silver Division is as good as in high division . But you would be squishy and most likely to be in great danger every combat . I suggest a more tanky build on him , since Silver Division lacks of Peeling and Positioning . I tried this build alot and it seem to fit in this Meta pretty dam well actually . Your early should be focusing around Rod Of Age and Tear , try to stack up the Tear around 25-minute mark . Then the rest should be optional , as i dont think Rabadon Deathcap is a solid choice . You Should go for something like Zhonya , Liandry is always a must , something like Luden's Echo and perhaps a Lich Bane . I have tried this build alot and it seemed quite effective against any kind of team formation . U could be quite healthy but in the same time dealing lots of damage .

AP kog relies on peel and good positioning. Since it's silver, just don't,

Depends. If you're confident the game wont end in 20 minutes I'd say go for it :p