I think there is some truth to this however at the same time I'm not sure the two situations are analogous. The Crusader army in 1204 was essentially combination of professional and peasant armies originating primarily from Western and Central Europe, financially backed by Italian merchant states. They were attempting to land in Egypt but ended up in Constantinople due to the Roman Empire not paying what Crusaders claimed that they were owed. I know that's an oversimplification, but the point is that by comparison, the Umayyad Caliphate was at this stage a comparatively far better organised, logistically supported and financed professional army-albeit still flawed in some areas (the plan to take Constantinople via the Aegean was a massive doctrinal misalignment).
The Crusaders weren't initially planning on conquering all of Anatolia or even Thrace itself, nor did they have the capability to do so. The Umayyads on the other hand and the Caliphate itself had proven to be more than willing and capable of conquering large swathes of territory and incorporating it into its domains either through vassalization or direct provincial administration. This included geographically mountainous and uneven swathes of land as well, such as most of (though not all of) the Iranian plateau. It's also important to bear in mind that Anatolia was, despite being mountainous like Iran, logistically much closer to the Umayyad base of power in Syria.
Whilst it is true that the Roman Empire was far stronger at this stage than in 1204, they were still undergoing major political issues. The Twenty Years' Anarchy coming to mind, and in fact being the period of instability that the Umayyads sought to take advantage of in their strategic gamble for Anatolia. It is quite plausible that with the loss of Constantinople, local rulers and nobles in Anatolia may simply see it as more beneficial to nominally submit to Umayyad rule and pay taxes to Damascus instead. A similar state of affairs occurred in the Iberian Peninsula, where following the destruction of the Visigoth army at Guadalete and capture of Cordoba, many other cities simply submitted to Tariq's terms with little resistance.
I do agree with you that there would likely be a great deal of resistance from some militias and local governors which inevitably gain more autonomy were Constantinople to fall to the Umayyads, however I find it unlikely that they would be able to launch a co-ordinated campaign of prolonged resistance, with anything resembling a unified Roman army similar to what Constantinople was able to launch in our time. I agree with you as well that that overtime, were the Umayyads to take Constantinople, they would eventually become the dominant power in Anatolia with most of the region coming under their vassalization at the very least, though it likely wouldn't be an easy task.