Tadley has a bit more of an orientation towards Newbury and Basingstoke. My husband grew up there (he stayed with his mum and dad and only moved out when he was around 34 having saved up for his own bachelor pad...that he only got to use as such for two years before he was no longer a bachelor

) and he talked a lot more about connections with those two towns rather than about Reading. There's a relatively good bus service connecting Tadley with Basingstoke via the hospital, which is in the same county and thus connected to the same education system, local government funding etc. He went to sixth form college (it's compulsory to move schools at that age in Hampshire) at QMC in Basingstoke.
Also you'd be going through Aldermaston to get there and that's very carefully maintained to keep the character of the village intact. Even the road signs are unobtrusive (of the old finger post style with just a hint of Worboys flair for consistency and visibility), so in an effort to connect somewhere that doesn't have much business with Reading and capture the market for them you'd be trying to run a tram through somewhere that won't necessarily take kindly to the metal rails and likely the perspex stands and so on. Sadly, the advantage of motor vehicles is that they only need a road laying. Trams and trains need a whole lot of other infrastructure that adds to the bottleneck that Aldermaston already is. The metal and glass and plastic needed would spoil one of the remaining unspoilt villages in the area.
The only benefit might be to make AWE more accessible. As you can imagine they've been running recruitment campaigns, but when I was jobhunting, I was offered an opportunity there but had to decline because of lack of transport. It might be better to link Basingstoke and Reading via Tadley, but then you'd be ploughing up half of north Hampshire to get it and buses start to look a bit more landscape-friendly.
As I also said on the last enthusiastic thread about trams, they're not the most comfortable mode of transport for longer distance journeys. Reading Buses generally uses single decker buses for SimplyNetwork routes (outside the core Reading area itself and with the exception of the 1 to Newbury) and it's possible to enjoy the ride out to Swallowfield on the 600. However, my experience even of modern trams elsewhere on the continent would make a journey as far as Tadley rather unpleasant. Motor vehicles have good suspension and relatively wide bodies and don't involve laying yet more clutter on the actual roads. Trams are good for short journeys in cities with a lot of contiguous urban or suburban areas (the whole Farnborough-Aldershot-Blackwater conurbation would be a good candidate).
But the Reading area has, as yet, not swallowed up outlying places, and you still have open countryside and areas that take cultural protection very seriously like Aldermaston and my parents' area to cross in a lot of places. Some of it is NIMBYism, but a lot of it is to try and stop Reading sprawling too far and keep discrete areas of human habitation in more harmony with the natural areas surrounding them.
I'm not against this in theory but in practice the landscape and infrastructure may not work too well together. It's kind of icing on a cake that's already perfectly iced. Focusing on bus routes for the villages (as well as a Sunday service of some kind) would be better and a railway station at Chineham would be the most practical solutions.