It is time for me to buy a pump and saddle bag to carry spare tubes and tire levers with me on my rides, as I have experienced a flat many, many miles from home, and it was not fun. I ride a Specialized Allez Double, and it has a curved toptube that makes me wonder whether or not an attachable pump would fit on my frame. Can anyone help me out?

You can attach it to your seat tube.

Will the saddle bag obstruct it?

Seat tube, not seat post =D. You will have to put it in front or on the side of the tube. It will not fit on the back of your Allez like in the picture.

Oh, duh, sorry about that, still a noob :/
But thank you, that is definitely an option

There are dozens of pumps that will mount to your bike using the water bottle cage screws. Most come with a piece that mounts under your water bottle cage (either cage, seat tube or down tube) in which the pump is held, allowing your water bottle cage to be usable as well.

I use these on my 2 bikes:

Could you provide a link to these pumps, or similar ones? Or just a name so I can search it?

I have a Lezyne Carbon Drive Mini Pump. It's works great and is about as sexy as a pump can be.

Another vote for Lezyne. I have, I believe, the Road Drive mini (or Pressure Drive?) - either way, it's tiny, works fantastic and comes with a bracket to mount it to your bottle-bosses. I have mine between the frame and bottle-holder, and it fits great - I feared it would stick out, but the bottle is wider than that.

It comes with a flexible bit that screws on in either Presta or Schrader, which allows you to pump without having to watch the precise angle to the valve. Fingers crossed, haven't had a flat since I bought it, but I tested it at home and helped a stranded roadie once - worked as expected.

The 2 I pictured are the Lezyne Pressure Drive and the Lezyne MicroFloor Drive. Lezyne makes many models that will work in different applications.

Really just search for things like "bike mini pump" or "frame pump". Lezyne, Topeak, Blackburn, Zefal, Planet Bike are all common brands, but there are dozens out there, all with different features.

I personally like the Lezyne pumps, especially with the very convenient screw-on hose even on the smallest pumps. I feel much less likely to break something than with other mini pumps, and it lets you get leverage more easily. Lezyne generally gets very high points for their design as well, and I'm a big fan of good design and good engineering.

I also use a Lezyne Pressure Drive. I actually carry it with me when I am working aswell (I am a bike courier). It has helped me, and a few other courier out a few times, The mounting bracket (which I have put on my road bike) is solid and very secure (I have even put a Topeak mini pump in the bracket and it has held on just fine).

I also vote for any pump that has a flexible hose. It allows you to safely inflate a tire to a higher pressure due to the fact that you dont have to worry about "slipping" when you are pressing hard and ripping your stem clean off.

I had my first flat with no tube or way to fix it too. I went the other route. Puncture resistant tires, an extra tube, and CO2 cartridges. Tube and CO2 fit in my bag vs a pump attached to the bike. Personal preference.

However, I'd be hard pressed to change a flat on the side of the road. I'd likely call the family or a cab for a ride first

I use a full size pump under the top tube. Spring compression keeps it in place.

Until I got a frame rack(the QR kind) I had mine attached to the right side of the seat tube. I ride a compact 44cm frame, and if I can fit it on that bike anyone can.

Another vote for the full-size pump that fits under the top tube. I have the Blackburn carbon one and love it.

My original question was whether or not a top tube mounted pump would work on my bike, as i has a curved top tube

You'll need a curved pump.