Probably fine in that sort of table, but you may need to drill mounting holes.
The Tufnol baseplate (thin brown plate, for sliding the router on normally) is held onto the base casting with four M4 countersunk machine screws. You can use these threaded holes to mount the router in the table.
If the table does not have holes in the right places already, you will need to drill them, and buy some longer M4 machine screws It is a bit fiddly but you only need to do it once, so take your time.
You will need a selection of new, GOOD QUALITY, "jobber" drill bits, up to at least 4mm size. And a new countersink bit, suitable for metal. The "snailshell" type gives a very clean cut, but doesn't last very long in metal. I recommend using a drill that can go at a very slow speed, as you need to start the holes accurately. One good way to do it is starting off with a hand drill and using a powered drill for the larger sizes.
Remove the baseplate. Mark the side of it that fits onto the router, in case it isn't obvious. You use this baseplate as a template to make the holes in the table.
Take the fences, etc., off the table and turn it upside down on some scrap wood.
Put the baseplate on top of the upside-down table, with the router side facing UPWARDS, and line it up so that the big hole in the table is central with the hole in the baseplate. Fix it down carefully - I'd use a lot of masking tape, but that's only good if you are gentle. If you find one of the holes comes close to an existing hole in the router table, it's OK to rotate the baseplate so this doesn't happen. But check, by standing the router in place, that you'll be able to get at its handles and the shaft and collet with spanners when it's rotated - the table legs will get in the way a bit, but you sould find a good position.
You can then use the four holes in the baseplate as a guide to carefully start drilling the holes in the router table. Personally I would just "kiss" the table with the 4mm drill bit, to make a good mark. The baseplate is very soft material, so be careful not to enlarge the holes in it with the drill! Check all four marks are central to the holes in the baseplate.
I would remove the baseplate at this point, and continue with a smaller drill, making sure it stays in the centre of the marks you've just made - keep dropping the baseplate into place and checking you're drilling correctly. When you've gone through, open the holes out to 4mm with bigger drill(s).
Turn the table over and countersink the holes so that your M4 machine screws fit with the heads slightly lower than flush. You're done!
You don't need the baseplate fitted to the router while it is in the table. You probably also don't need the springs on the columns, as it's not plunging - taking them off makes it easier to adjust the height.
It's very easy to slip when drilling, and get the holes slightly wrong. If so you can probably open them out to 4.5mm through the table, but I wouldn't go bigger than that.
I have never had a router come loose in a table, but there is always a lot of vibration. Check it is tight after a bit of use. If it's coming loose you have some options. I don't know the T3 - if the baseplate holes go right through, you might be able to fit locking nuts on a longer machine screw (after the router base). If you can do this use "Nyloc" nuts as they won't vibrate loose.
Otherwise use a drop of threadlock (from a car spares shop) on the countersink before you tighten everything up. It will creep down the thread towards the router baseplate, and should stop the vibration effect without gumming everything up permanently (that's what it is supposed to do).
I quite agree about fixing the table securely, especially if you are finishing the edges of wide or long boards, and about the car jack - lots of people do this and say it works well (you may need to leave the springs in place if you do it).
Hope that helps.
E.
PS: if it is not a new router, it would be a good idea to get a new collet to start with. Worn collets cause cutters to work loose and damage their shafts. This is both dangerous and gives a poor quality cut. One good thing about the T3 is that spares shuld be easy to get, so I would start off that way.
Also, when shaping, pay attention to the cutter rotation speed, and the rate you feed the wood through. If the cutter is too fast, or you feed too slowly, you will get burning. Practice and experience will show you the right speeds.
