IL-1beta is produced as pro-IL-1beta which requires a second "danger signal" to induce productive cleavage and release. This is true for most cell types and so the answer is: No you don't need to block the secretory route to detect IL-1beta intracellularly.
Do you want to detect mature IL-1beta or just accumulation of pro-IL-1b? Either way, this is a tricky question. I might be wrong but I think that Golgi stop is not going to make too much difference, even if you fully stimulate the inflammasome complex in your cells.
As you know, IL-1b is synthesized as pro-IL-1b which then requires assembly of the inflammasome complex and the cleavage of the IL-1b precursor by active caspase-1. The cleavage is usually done in the cytosol or in secretory lysosomes. After that, multiple pathways exist for the processed IL-1b to exit the cell. Most of these pathways are actually non-classical secretory pathways. For example, when the cleavage is done in the cytosol, mature IL-1b can be released by plasma membrane microvesicles (blebbing) containing caspase-1 and IL-1b, or by direct release via protein transporters of the plasma membrane. When the cleavage occurs in vesicles is because pro-IL-1b is transported to previously formed secretory lysosomes, where co-localizes with caspase-1 and then it is processed and released together with caspase-1. So I would say that inhibiting the Golgi transport system would have little impact on IL-1b secretion anyway.
Something similar happens with IL-1alpha. At the beginning it was thought that IL-1a was not under the control of the inflammasome, but recently it was shown that inflammasome activation is necessary for IL-1a secretion (PNAS. 2011 Nov 1;108(44):18055-60.). And it seems that the secretion of IL-1a is also controlled by Golgi-independent mechanisms.
In addition to the comment above I would like to mention that most antibodies are not specifically directed to the cleaved (active) form of IL-1beta. So during flow cytometry you will only be able to see the total amount of IL-1beta in the cell, which is not neccessarily related to the secretion of the active form.