The US and world powers would not interfere because there is little to gain for them
But don't you think Senegal can invade Somalia, or do you think the somali army can chase senegal out? both armies similar in size but senegal has a small air force
They would definitely be involved, they're propping up the current government and are dropping bombs on "al-shabab" areas.
I think if Senegal was determined they could invade somewhat deep into somalia, probably until galkayo. This is because somalis right now have horrendous morale and unity. Similar to the Iraqi's when Isis took over.
The problem is that Senegal has about 20,000 men. They could never sustain any kind of occupation, their numbers are too low.
The locals would do guerilla warfare. It would essentially be a lot of wasted time, money, and blood with no longterm gains. Just like the U.S in afghanistan, Iraq etc.