If you run them inside to protect them from the elements, probably yes. You need to check the user manual and technical specifications for the instrument you have.
I think the question is a bit misleading, are you asking if the instruments you use for ozone monitoring for outdoor environment can be use inside? which I believe is possible given that the environment inside complies with what is required in terms of ventilation, space, etc.
Or are you asking if there are any instrumentation to be used inside? Take a look on this one which has been designed by a young man: http://www.naqts.com/
I dont know if it measures what you require but there are options for sure.
The correct answer is - it depends. You must consider, for example:
(1) Is you monitoring for regulatory purposes? Most indoor air monitoring instruments cannot meet the stringent requirements set for regulatory ambient monitoring.
(2) Detection limits and detection range. Indoor environments often have high concentrations of air contaminants than the ambient.
(3) Can the instrument work properly in harsh outdoor environments (e.g., precipitation & wind)?
As Xufei said it does depend heavily on what you are looking for and your limits of detection.
I work with analytical thermal desorption instrumentation which is specified by a number of different regulations for monitoring of VOCs in both ambient air (EPA methods TO15, TO17 & 325) and for use in VOC measurement in indoor environments (ASTM D7339, ISO 16000-6, ISO 16017-1&2).
So if you were hoping to measure VOCs ranging in volatility between acetylene and C44 then in the majority of cases methods can be transposed between indoor and outdoor air with little effort.