Can vascular conditions cause spleen damage?

It depends. It depends what you mean by vascular conditions. Vascular conditions (aneurysms, dissections, strictures, etc) are very unlikely to cause spleen damage. On the other hand, certain blood diseases can clog the "filtering" capacity of the spleen and damage it.
Splenic aneurysm. Trauma, cancers, infections and other causes are the main indications for spleen removal. A splenic artery aneurysm can be treated with medical management and observation if it is small. If it grows rapidly or over 2.5 cm a stent, coil or spleen removal are treatment options. So indirectly, the answer to your question is "yes". It is rare for vascular ischemia/lack of blood flow to affect spleen.