Perhaps - though I suppose it depends on what they (the Ukrainians) are countering them with. From the footage today it seems its volume of fire from rifles and above, which wouldn't be much of a drain on resources.
What they're countering it with will depend on the altitude. They're pretty slow (100mph-130mph) but apparently have a service ceiling of up to 3,500ft.
They may fly lower than this, but it's not beyond the realm of possibility that it'll exceed the effective range of most rifles in the Ukrainian arsenal.
So we're talking about heavier calibre weapons, and that would need to be in the right place; to get coverage, it'd be really, really difficult to effectively do so.
Additionally, it's very costly to shoot these things even with MANPADS, let alone larger defence systems. You're talking about tens of thousands of dollars.
They'd offer better coverage, but it is worth wasting these weapons against what's likely to be affective against soft targets, with the key ones already defended.
It may be great to hit them down for kudos, however until a system can adequately put in place I think they'll let a few through and perhaps take the hit.
To waste their arsenal on them is exactly what Russia will want, as they'll have a better chance with their fixed wing aircraft and cruise missiles.