Can I swap the logic board with a 2009 MacBook?

You mean the model numbers... I think the graphics card/display LVD connectors could be problems. Look at them visually for connector/port mounting screw differences.

Externally, the "Early 2011" and "Mid-2010" lines unfortunately use the same model numbers as several earlier MacBook Pro models and EMC numbers are not listed at all, so they only can be externally differentiated by the last three or four characters of the serial number courtesy of EveryMac.com's Ultimate Mac Lookup feature (the last three characters for models that have eleven character serial numbers and the last four characters for models that have twelve character serial numbers).

A general rule of thumb is logic boards most often swap between the same, but not different years of manufacture... sometimes the difference between early, middle and late are enough to cause incompatibility

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