Following the following sentences that you posted
1)I went to work -and so had Mark and Tom.(meaning I went to work, and Mark and Tom also went to work)
2)I'll go to Beijing -and so will have Mark.(meaning I'll go to Beijing, and Mark'll also go to Beijing)
Yes,you understand the meaning exactly: this pattern is for showing ADDITION to something that's already been mentioned!
However, there's an error in #2, so I don't think you quite understand how the pattern works.
Notice in the following that the auxiliary verb in the "and so..." part depends on the main verb in the first part:
"XXX ATTENDED the meeting, and so did YYY."
"XXX WAS at the meeting, and so was YYY."
"XXX AND ZZZ ARE at the meeting, and so are YYY AND QQQ."
"XXX MIGHT /CAN/MAY?SHOULD attend the meeting, and so will/can/may/might/should,etc. YYY."
"XXX HAS MADE a presentation, and so have YYY & amp;ZZZ/has YYY."
"XXX HAD ARRIVED before the boss, and so had YYY."
"XXX WILL HAVE MADE his presentation before the boss arrives, and so will YYY."etc.
So, the rule is that the auxiliary verb in the additive part must match the verb in the first part.
