Whether or not this is possible foryou depends upon which provider you are using and how they arrange their channels on their satellite transponders (which is why I suspect Anders used 'in theory' and 'in reality' in his response).
TVHeadend can stream/record every single channel carried on an individual multiplex/transponder so one tuner can stream as many channels as that multiplex/transponder carries. For your specific situation, it depends entirely which channels you are expecting to stream and whether or not they sit alongside other channels you want to stream.
As an example, in the UK, we have a national DVB-T network, one of the multiplexes carries the five national broadcasters HD services (BBC One, BBC Two, ITV, Channel Four and five) all alongside each other. This means that it's possible to stream/record all five of those channels at the same time whilst utilising only one physical tuner.
To get a better understanding how how many channels you can likely squeeze out of a single tuner, refer to http://www.lyngsat.com and look up your provider, this will give you a multiplex/transponder list for your provider and show you which channels are carried by each - you can then work out how many channels you'll be able to get from a single tuner.
BUT Anders is absolutely spot on that you can only tune into a single frequency (multiplex/transponder) so all the above is only true if all your clients are requesting channels from the same frequency - if one requests a channel that's carried on another frequency, TVHeadend will return a 'no free tuners' error.
Working example:
Multiplex one carries: Channel A, Channel B, Channel C
Multiplex two carries: Channel 1, Channel 2, Channel 3
Client 1 requests Channel A: The stream begins
Client 2 requests Channel B: The stream begins
Client 3 requests Channel 1: TVHeadend returns 'no free tuners' error
Only when all clients have stopped streaming will TVHeadend allow another client to tune to a different frequency, at that point all clients will be limited to channels from that frequency.
Hope this makes sense.