Can Tatsuya use Material Burst in the tactical/strategic scale without the Third Eye CAD? The "Third Eye" CAD is treated security-wise like a nuclear detonator, and custom made by third division of FLT exactly for him use Material Burst effectively.

Is it feasible for him to cast it at that scale/range without it?
Yes, he can maintain strategic class levels of range and potency, even without the Third Eye.



There are two parts to strategic level magic - range, and strength.

Tatsuya can successfully cast Decomposition on objects with the size and mass of Armoured Personnel Carriers (APC's), and material burst is merely an differentiation of that (the conversion of matter to energy, rather than base elements). A flag of 1kg is the cause of the destruction in Zhènhai Naval Port, so while he would find no trouble in casting Material Burst on something like a car, the destruction caused would be far greater. 

Being near the activation point of such a cast would be, as mentioned in Saphiric's answer, suicide. But, this is just hypothetical - Tatsuya has the potential to cast that kind of magic if he wanted to, and that's all that matters for the question.

So his scale, naturally, is still of strategic class even without the Third Eye.



Range is a more awkward matter.
While it's more difficult for him to activate magic on a strategic scale without the Third Eye CAD - mostly due to the necessity of finding a suitable target - it is still possible for him.

It's important to remember that magic isn't bound to the physical plane, instead using a separate dimension where trivialities like distance aren't issues. Since magic is simply a phenomenon rewriting the data of a specific Eidos (information body) that exists in the real world, as long an information body's coordinates are known, it can be targeted.
Only a very small number of spells (such as Gram Demolition) physically travel through the real world, and therefore only those spells are restricted by physical distance.

Most magicians can't perceive a target more than several hundred meters away, simply due to the limits of the human body.
But, this is Tatsuya. With his Elemental Sight, he can perceive things in the information dimension, or the dimension of magic, where distance is no issue:


  This was not looking down from a bird’s eye view, he was looking at things from the point of view of the information dimension. It was not an elliptical sphere around the double focal points, it had nothing to do with physical distance[...]
  
  Volume 10 - Visitor II, Chapter 12


Even so, he can't just pick a random target to cast Material Burst on - he has to know the coordinates of the Eidos. This is the main purpose of Third Eye, to pick targets at huge physical distances, so Tatsuya can easily manipulate them in the information dimension.
However, this isn't the only way he can find a target. If he picks out an information body he can perceive at close range and follow it as it travels, he can cast magic on it at any distance:


  By his own hands, using the magic he alone could wield, he had decomposed then
  rebuilt the bullets. However far away they flew, he would not lose sight of their information structure.
  
  Volume 8 - Reminiscence,Chapter 16


As proof of this, the first time Tatsuya uses Material Burst is without any sort of CAD, and he casts it at a target 20km away, one of the aforementioned bullets:


  Tatsuya stretched out his right hand towards the west, and forcibly unclenched his palm.
  
  The bullet broke down into energy.
  
  In that moment, the mass conversion magic ‘Material Burst’ was used in anger for the first time.
  
  Volume 8 - Reminiscence,Chapter 16


Granted, it's not quite as far as the distance he casts it in Episode 26 of the anime, but it's still a considerable distance that's far beyond the realm of normal human perception. Furthermore, he states that he could cast it at a greater range, but in this instance, he is limited by the range of the sniper rifle's bullets he uses as a medium to cast Material Burst on:


  Sanada’s murmur was drowned out by the boom of the sniper rifle.
  
  Tatsuya’s eyes seemed to chase that supersonic bullet which should never have been seen.
  
  At length he shook his head, disappointed.
  
  "……It’s no good. It could only reach 20 km."
  
  Volume 8 - Reminiscence, Chapter 16


So although practically very difficult to recreate without proper planning and requirements, it is theoretically possible in the right circumstances, meaning his range too, is still that of strategic class without Third Eye.



In conclusion, yes, Tatsuya can cast Material Burst unassisted at a range and scale similar to that which he achieves in Episode 26 with the Third Eye, but he would require a very specific set of circumstances, and would need to rely solely on Elemental Sight for targeting. That's the main reason for that CAD - to make Material Burst far more practical to cast.

With or without Third Eye, he's still very much "Strategic Class"