SO the British getting to Tripoli before the Germans isn't going to happen. No matter what there will have to be a halt somewhere. The British do have quite a lot going for them ITTL however.
As it stands we are 3 weeks ahead of OTL. If nothing else changes Britain will reach El Aghelia on the 19th of January. Not that other things wont change. The faster advance will likely catch Italian units and positions completely flat footed.
The captured Italian trucks will be a great help, yes not all of them can be put into service straight away but while not ideal is not much of a problem. Having the ability to put a few into service straight away is a nice bonus but also having a reserve of trucks isn't a bad thing. As the British trucks wear out and break down it becomes possible to train the driver on the Italian trucks and put him back into supplying the WDF. This sort of thing has already been considered see here
The windfall of Italian trucks was much needed, but these were unfamiliar to their new owners, and all too many were wrecked or damaged by ill-use. General Hutchison had hoped for the Italian windfall, and with his contacts in Cairo and elsewhere tried to get some RASC men trained in the use and maintenance of the Italian makes and models, as some of these were present in the civilian population. This would pay off over time, but the immediate needs were the priority.
So while you aren't getting a massive surge of new(ish) trucks instead you hopefully have a much more consistent level of supply across the campaign. This will only improve as time goes on as more and more people get familiar with the Italian equipment and ports closer to the front open up reducing the wear on the trucks.
What does this all mean, well a quicker resumption of the advance. Britain can't just decide it is going to Tripoli and set off. Supply dumps and maintenance stations lines of communication etc need setting up on the way. How easy this is depends on what sort of resistance the Italians are able to mount. If they aren't able to mount any sort of serious and organised resistance the British will know. Patrolling will give the British an idea of what is in front of them and it likely won't be much. At that point while a large portion of the WDF may sit in place resting and refitting before the next big move I would not be surprised to see a smaller formation sent ahead to capture convenient locations for supply dumps etc. Think of it as a reconnaissance in force that is laying the groundwork for the main force to move up behind. Then when the main force does mover it has supplies of food, POL and water ready to supplement those it is bringing with it. How far that advance force Might go depends but Sirte is as good a place as any to aim for and set up a more permanent base of operations to launch the next push from. It is pretty much half way from El Aghelia and Misrata so as a point to move the main force too before starting the next push it may well be considered convenient.