How can I tell if the size of a bike is right for me?
Frame fit

Primarily, a bike fits if you can position pedals, saddle and handlebars relative to each other so that they match your body's proportions. Secondarily, when these contact have been set, other frame parameters should fall into place so that the riding characteristics are as desired. That includes e.g. toe clip overlap, stand over height, bottom bracket height, heel/panniers clearance, steering geometry, or that an extremely short or long stem gives a weird steering balance. Depending on what you use the bike for, the importance of these parameters varies.

Does "frame size" equal "seat tube length"?

If you consider frame fit as putting the contact points in the right spots, the length and angle of the seat tube is one of the less important dimensions. By choosing the right seat post length and setback, it is possible to put the saddle in the right position relative to the pedals (or, simplified, the bottom bracket). Generally, on most frames, most riders can put the saddle in the right position relative to the bottom bracket.

Depending on the use of the bike stand over height (or clearance) is more (MTB) or less (road) important. If you want a certain stand over clearance, of course this limits the frame size to a certain amount. This is easy to determine: With the correct tires and wheels, the height of the top tube should be lower than the length of your inseam.

How to determine "frame size" instead

The critical point is often if you can put your handlebars of choice in the right spot, too. One thing to consider here is that drop handlebars have a significantly longer reach than straight ones. This is because the normal hand position is on or behind the brake lever hoods with a drop bar, and not on the straight section next to the stem eye. If one does not want to resort to extremely short or long stems, a frame usually only allows for a good fit with either drop or straight bars.

Working backwards from the hand position through handlebars and a normal sized stem (ca. 8-12cm on a classic frame like this), one ends up at a certain position where the top of the head tube should be.

Stack and reach

The corresponding frame dimensions are the vertical and horizontal distances of the head tube upper end from the bottom bracket, called stack and reach. Unfortunately especially frame reach is quite difficult to measure on a frame without complicated measurement setups (or a good picture exactly from the side without perspective distortions). Therefore many tend to use top tube length as an alternative to reach, and ("virtual") seat tube length instead of stack. One should be careful though: The position of the top of the head tube not only depends on seat tube and top tube lengths, but also on the seat tube angle (which can be even harder to measure than reach).

The easiest way to find out your needs regarding stack and reach is to measure a bike which fits you well and has the relevant handlebars setup. One way to do this is to take a photo exactly from the side and from quite far away, and measure in the picture.

What does this mean for you?

As you say, stand over clearance does not bother you with this frame, so the seat tube length is very likely ok. On the picture there is also plenty of room to move the saddle forwards, in the worst case with a zero setback seat post. So the saddle probably position fits you. Good.

I am more concerned about whether the frame reach is too long, when changing to a drop bar. But as far as I know, the classic Raleigh road geometries do not have overly long reach, and the stem shown on your picture is way longer than what I would consider aesthetically pleasing on a frame like this (especially with quite little seat post to be seen).

Without knowing more about the frame and your fit preferences it is very hard to advise if it will fit you in this regard. The fact that the frame was built with a classic quill stem in mind, but has a threadless fork today, does not make it easier: It may be that you can't rise the bars enough with an ahead stem (and the fork already being cut).

The easiest thing would be to just try putting a drop bar on the frame (ideally with an adjustable stem temporarily). With a fixed gear that should be easy to do. Ride and adjust, and you will feel if it fits.

What else?

Apart from all that I think that the average 56cm frame is quite a bit too small for the average 1.88m male (horizontal top tube, or "virtual seat tube length" assumed). I am 1.83m myself and usually start looking around what is labelled as 58cm.

I'm pretty sure that the fork is not original. Ask the seller if the original still exists. It probably is a threaded fork, which allows for higher building quill stems. And it probably looks nicer, too.

Finally: I have never heard about problems with the thighs rubbing on the seat stays before...