The splitter should work but your tube preamp's output will be driving a lower and lower effective impedance as you add amplifiers. That could pose an issue, especially for a tube preamp because they tend to have high-ish output impedances.
RCA Splitter to convert a single RCA output into two
I would like to connect a single RCA output of the tube pre-amplifier to drive two monoblock amplifiers (instead of just one). Would it be "safe" to use the RCA splitters such as the ones offered by Audioquest without a risk of introducing any sound quality degradations or making a harm to the system? Is there any limitations on how many RCA splitters could be used to split a single RCA output? Would it be safe to chain the multiple splitters to split a single RCA output into three, four or even six RCA outputs to drive multiple power amplifiers?