If I have an ad-hoc DOE design, say one I made by hand in excel, is it possible for JMP to perform the diagnostics on this design? E.g. to show optimality for aliasing, variance estimates and so on?
Yes, the Evaluate Design platform in JMP 10 will give you design diagnostics for an existing experimental design.
You can judge aliasing (actually, correlation) of the predictors via the Multivariate platform. You may have to add interactions and squared terms (etc.) into your data table.
The effect on variance can be seen by turning on the Variance Inflation Factors (VIF) in the Fit Model Parameter Estimates table. (You can create random Y values if you want and then evaluate the design prior to collecting the data, as the VIF doesn't depend on Y)