Hi Noah,
Whilst a pressure bleeder (Gunsons Ezy-bleed), or a suction pump would help - it is probably not "necessary"..... certainly if you have an assistant - or preferably 2 - on hand.
One thing with the Elan system is that the fluid levels in the master cylinder reservoir don't tell the real picture unless the car is absolutely level - ie, all 4 corners the same height. If you have the rear up in the air, with the front on the ground, it can be difficult to get enough fluid into the rear chamber of the reservoir to bleed the rear brakes..... or, at least, it needs watching carefully as the reservoir appears to be pretty well full when the rear chamber drops, and doesn't refil from the front due to the height of the separating dam.
If you have 2 assistants it can be done with the rear in the air, one to press the pedal steadily, and one to trickle new fluid into the reservoir to keep the levels high enough..... It can be done with one assistant, but needs some athletic endeavour to keep an eye on the rear nipple and the front fluid levels.
So, it is actually a little easier without an assistant to nag at you as to why you are running around and that their leg is getting tired holding the pedal down etc etc.
If you simply attach a clear tube to the rear nipple and open it (other end in a jar) and with the reservoir cap off, just go and have a cup of tea - or push the pedal once if you want, then top up the fluid... gravity will bleed it all for you. Repeat with the other rear, then the front...... or if you have 4 bits of pipe and 4 jars, you can do all 4 corners at the same time - but you need a close eye on the MC levels as it can change quite quickly........ I have left my car overnight before now with the nipple only slightly open to clear an airlock, and it was fine.
In real terms, the 'gravity' system won't shift stubborn trapped air as there is only a slow flow of fluid - but it will fill the pipes enough to give you a pressurised system to do it the traditional way if required.
I understand that the Honda callipers at the rear don't trap air in the same way that the OE ones do, but you may still get a bubble or 2 in the proportioning valves, so tapping them with a spanner whilst bleeding may help.
10-20 minutes of gravity should see fluid emerge from the nipple(s), and is my preferred method of doing the job (because I can sit and drink tea whilst occasionally topping up the fluid

) - but it works because once the pipes are attached, the car can be dropped to the ground to keep it level and make the topping up easier - it is possible to (just about) get to the nipples enough to screw them in and stop the fluid with your fingers, then jack up the corner and get a spanner on them to do it up fully when all 4 corners have finished.
The only real advantage of a pressure system is that it will keep the reservoir topped up for you - and that is worth it's weight in gold really (as long as there is a good seal and you don't get fluid thrown everywhere from a leaking rubber washer) - but a suction system doesn't do that, so I feel, it is of limited value anyway.