yes, in my experience and research, spider mites damage the plant substantially if left unchecked/uncontrolled no matter the plant's growing stage...there is some evidence that spider mites are either the vector for black tip, or they weaken the tip tissue enough to make the plant susceptible to fungi, like the one causing black tip and keep the blooming cycle repressed.

A commercial plumeria grower told me that he is certain they are the cause of black tip in plumeria and similar tip necrosis in adeniums.

I would take care of them immediately...dyna-gro neem oil or a similar product diluted in H20+ a surfactant like dish soap does wonders. I have even used other plant oils like olive oil and canola when I ran out of neem temporarily and they seemed to work also. Neem (cold-pressed not the hydrophobic extract) is the best though as it contains azadirachtin, a compound that has proven insecticidal characteristics. Apply every 3 days for two weeks, then PRN.

good luck and keep us posted on your mite war!

-stephen

Here is a link that might be useful: spider mites

Yes. They feed on sap from the phloem stream, which is to say they suck out the carbohydrates (food the plant has manufactured and uses for growth and to keep its systems orderly) that sustain the plant.

Al