Yes, compliance can be monitored without "spot-checks" at military facilities. Much like with racial profiling (as opposed to behavioral profiling), such a technique is essentially throwing resources at random targets with the hope of eventually striking a bulls-eye on a target that they didn't know existed.
That process would be a waste of valuable resources that could be used in effective monitoring activities.
The IAEA has a vast array of practical knowledge, surveillance tools and intel from surveillance programs of other nations to help it determine when activity outside of declared sites might be happening.
Keep in mind that all uranium production, world-wide, is tightly monitored and scrutinized. So for Iran to try to enrich any material they'd either have to acquire new material, which would be difficult, given how it all has to be accounted for from mine to delivery, or they have to divert materials they already have, which would be detected by its absence at declared sites from declared stockpiles.
This still leaves open a gap of Iran doing all of the surrounding work in building and preparing a facility, except for the fissile material, and then, if they declare that they are done with the deal, they are pretty much ready to roll and can begin diverting material to production-ready sites.
So, in addition to materials monitoring, the IAEA has to be aware of steps that a nation would have to take to prepare, and to monitor for that kind of activity. How do they do this?
Iran has mastered centrifuge enrichment technology and has constructed undeclared—that is, clandestine—enrichment plants. It is possible that Iran has other facilities that have not been detected. These facilities could include centrifuge production plants; plants to convert concentrated uranium ore, known as yellowcake, into uranium hexafluoride, the chemical form required for enrichment; one or more enrichment plants; plants to produce highly enriched uranium (HEU) metal; machine shops to produce warhead components; and plants required to produce all of the remaining warhead components. Because natural and depleted uranium are identical to HEU in chemical and metallurgical properties and are relatively easy to acquire, the steps required to produce nuclear warheads from HEU can be rehearsed well in advance so as to be ready when required.
Although the risks of being discovered by Iranian dissidents, national intelligence services, or the IAEA would be substantial, Iran could choose to construct new facilities after the new agreement enters into force, using its experience to conceal the construction and operation of such sites. The expertise developed at its declared enrichment plants and centrifuge manufacturing plants would give it an enormous head start.
The IAEA has a satellite imagery analysis unit with extensive contracts for commercial imaging services, and further improvements of this capability, including enhanced optical resolution, infrared and radar imaging, automated change detection, and ultra-high definition video streaming, are being pursued through IAEA support programs. The ability of the IAEA, bolstered by national intelligence programs and possibly Iranian dissidents, would make constructing a new enrichment complex like Fordow unlikely.
Given Iran’s knowledge of satellite imagery capabilities, if Tehran were to create new clandestine facilities, it might try to hide them in cities, possibly under industrial facilities, hospitals, or shopping malls, or on military bases rather than building them underground in remote parts of the country. National intelligence services employ methods, such as spying and intercepting communications, that are beyond IAEA capabilities. States share their findings with the IAEA in part to allow the agency to pursue inspections on the ground, using its legal authority under the watchful eye of the international community. Combining detection efforts in these ways would increase the chances that clandestine facilities would be detected if Iran were to choose to construct such facilities.
................ If the IAEA receives the support it needs, which is likely, it will be able to verify Iran’s commitments effectively. Even the skeptics should have confidence that if Iran changes course, IAEA verification will work in time for intervention to prevent Iran from acquiring a nuclear weapon.
Arms Control Association - The Verification Challenge: Iran and the IAEA (June 2015)
Compliance is much more likely to be successfully monitored if additional site requests are based on targeting by cause, not randomly, even if the authority existed to request inspection on a site, "just because." Keep in mind that this program is already more intrusive and contains more concessions by Iran than any nation has ever agreed to. It is unrealistic to think that any sovereign nation would acquiesce to intrusive inspection of sensitive sites when no evidence or cause for inspection can be given. From a politically practical point of view, and from an objectively analytical point of view, the idea of trying to impose random spot-checks of military site, based on no evidence, would not help to improve compliance monitoring.
