A sheilding can around the tube will make a difference to the incidental capacitance ,
Heat dissipation and air flow may also be effected by the presence of a tube shield .
In one mic I made I used aluminium tube with an ID very close to the tube diameter I was using , it turned out some versions of the EF86 wont fit in , the Mullards fit , the later East German/Russian varieties dont .
The aluminium part the tube fits into is bolted to the the frame ,so has a chance to dissipate heat by conduction .
You do see some better domestic tube gear with very close fitting mu metal tube sheilds , they have a short lenght of braided wire making the 0V bond at the appropriate point in the circuit .
Tube reel to reel players from Tandberg have it , the reason is that both a motor and power transformer are in close proximity in a tape machine ,so extra precautions need to be taken to exclude the AC feild .
Anyway in the context of a hi-z tube mic the proximity of the tube screen will have an effect on the tone , it might be favourable or not depending on what your trying to achieve .