There may be some benefit of a time delay device if you use an amp with a solid state rectifier. If your amp uses a GZ34 rectifier, however, then IMHO a time delay board is not needed. The GZ34 rectifier tube is indirectly heated and needs about 15 seconds or so to warm up before it applies any high voltage and when it does apply the high voltage DC > it comes up slow. By that time the tube heaters are all lit. Any time you use a GZ34 rectifier you have a "built in time delay".
If a 5U4 rectifier is used the high voltage comes up a little faster because a 5U4 is directly heated but even a 5U4 (or for that matter almost any tube rectifier) won't apply the high voltage instantly like a solid state rectifier.
That said, Dynaco used solid state rectifiers in both the ST-35 power amp and the SCA-35 integrated amp with no time delay and many of them are still working fine.