So is that good, bad or indifferent if the SACD signal is sent through the HDMI or does it depend on the receiver?
It depends. It is certainly more convenient to use the digital connection, assuming one has the appropriate equipment that can handle such a connection. Some SACD players convert the DSD to PCM for sending through the HDMI, but some also convert to PCM for internal processing when using the analog output anyway. It should make no audible difference doing this, but those who imagine that SACD is superior to DVD-Audio are likely to object to the conversion. Certainly, other than convenience of managing the signal, there is no advantage to convert between these formats of digital.
As for whether it will make an audible difference to use the analog or HDMI connections, in most cases, people will not be able to conveniently level match the signals and therefore will not be able to conduct anything approaching a fair listening for themselves. Theoretically, what you would want to do is use the device with the best D/A convertors, though if the receiver converts the analog input to digital for processing, one would not be eliminating the receiver's converters from the signal, and one might as well use the HDMI connection, even if the converters were better in the player.
If you are dealing with good equipment, you will not be able to hear a difference between the analog and the digital connection, assuming that you properly level matched the signals for the comparison, and assuming that you do not apply different processing to them.
So, I would suggest that, in most cases, it would be best to just use the HDMI, as it is likely to be easier. You can, of course, try both, and do whichever you prefer, though, as I already have said, without properly level matching the two different signals, you will not be able to do a proper listening comparison anyway, so there generally won't be much point in trying both.
Also, from reading various professional reviews online (in which measurements were made), if one is using a cheap SACD player, probably the receiver will have better D/A conversion, and better analog circuits, so using the HDMI connection in such a case would be best.
I have a fairly well regarded SACD player, but if it had the HDMI connection, I would use it.