Thermocouple socket wrong way round on board - problems?
It's tricky reasoning about thermocouple junctions, so it's worth going back to basics. This is the conventional temperature practical measurement situation.







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The voltmeter reads Tmeas-Tref. The introduction of disimilar metals into the thermocouple loop does not matter as long as both Tref junctions are at the same temperature. 

When we remove the copper wire and voltmeter, as the junctions are at the same temperature, and move the voltmeter somewhere else, then we get the classic thermocouple diagram from basic physics text books, where the voltmeter obviously reads Tmeas-Tref.







simulate this circuit

In plugging the thermocouple into the socket backwards, what you are proposing is the following







simulate this circuit

The voltmeter reads Tmeas + Tref - 2*Tsocket

Any difference between the socket temperature and the reference temperature will be added two-fold to the measured temperature. If that difference is expected to be &lt;&lt;0.5C, then you may get away with it. 

If not, then it would be better to plug the thermocouple in the right way round, and modify the firmware to negate the measured difference from reference.