Per the option laid out in the OP the British were so small in number that rolling in with a limited force that was heavily motorized could be sustained deep into Egypt, as at the start of the Italian war they had the best supply options available of any time of the North African conflict due to Malta not yet being up to speed, the pre-war ports of Torbuk and Bardia being well supplied, with supply stockpiles, and being at peak capacity before both sides swept back and forth over the ports and sabotaged them.
The big problem for the Italians in 1940 was moving into Egypt with a lot of foot infantry that were logistically unsustainable. Had they opted to move light with only motorized forces they would have had a much better logistical situation, especially by stripping out all transport in Libya to move supplies and the limited number of men around.
The issue I see with this is as follows
The Italians doing what you propose can probably form 2 Armour Divisions - each with - 1 Armour Brigade with 3 Battalions (1 Regt) of L3 tanks*, a Brigade of Lorried Infantry and some towed artillery.
*I think they had something like 330 L3s in Libya in June 1940
Against this the British have 6th Infantry Div HQ, 4th Indian Division and 7th Armored Div plus I thinks it was 2 Cavalry regiments (= 2 Battalions of Armoured cars) and about 1 Brigade of the NZ Division + its First Echelon
Now granted the British formations are both initially understrength and spread out - but their equipment and training is far superior to those of the Italians - in addition their 2nd and 3rd Echelons are far more capable.
And most of it had been training in the desert for 2 years or more.
The tactics the British planned on using was to initially fall back along the coast delaying and inflicting losses to the mass of the 10th Army while destroying the road between Matrah and Sidi Bahrani (which I assume to be Bridges, viaducts etc) behind them while building up forces to defeat them at say...Mersa Matrah where the rail head ended or even further back towards El Alamain.
Faced with a similar sized force with inferior equipment and training the British are instead going to initially fall back and once content that they are not facing the Entire 10th Army turn and attack.
Given the disparity in Equipment and training I would expect this to result in the defeat and very likely the effective destruction of this Italian Mobile force.