Ah, the Tele! One of my favorite subjects. Philboyd and Bongolation have both added some great info. Hopefully, what I say will augment their views a little bit.
First, in regard to a Strat sounding like a Tele, you can get in the ballpark, but it still will be different. For one thing, the Tele uses strings through the body, where a Strat uses the tremolo block to attach the ball ends of the strings. The energy transfer is completely different.
The Tele bridge assists with that transfer as well. With the old stamped steel bridges, it also adds resonances. Those bridges also can contribute to feedback if they are not fastened down properly. The big brass saddles really do add to the tone as well, and I recommend them over the stock steel saddles, especially the low strings.
This next thing--I have no proof other than experimentation--but the different body shapes resonate differently. The Tele has its own sound. So does the Strat. Changing pickups in either will alter the tone, but you can't really make one into the other. By the way, my personal opinion is that the Teles with the ash bodies have the most authentic twang and tele tone. However, try before you buy. As we all know, every guitar is different!
As Bongolation mentioned, the maple neck is a factor in the tone. The maple necks seem brighter and seem to push the notes out a little more. Still, try some rosewood neck models. You might like that slightly warmer sound better.
Last, the pickups. The neck pickup is not really a lipstick pickup. Its like a small Strat six pole pickup with a metal cover, just for the record. These single coil neck pickups are very prone to feedback if you play with lots of distortion. The bridge pickup is the real tone producing beast of the Tele and it mixes well with the neck pickup, creating a present yet fatter tone with both pickups engaged. By itself, the bridge pickup is cutting and very bright. Many players roll off a bit of the tone control to compensate.
As for pickups themselves, I have been through a ton of them. I have tried probably ten different brands of pickups for the Tele. If you are a single coil purist, try the Fender Vintage Tele in the bridge. If you are like me and record around computer monitors a lot, you might want to look into hum cancelling pickups. I ended up with
the Joe Barden's and I like them a lot. All the twang and high end and no hum. For the money, the Fender noiseless ain't bad.
The secret is to find a good sound sounding Tele to begin with. The physical guitar is as responsible for the sound as the electronics. If you find a good one and get into the vibe of the Tele, you'll find its a very versatile, yet unique instrument unlike any other electric guitar. I hope you enjoy yours as much as I have loved mine over the years.