I guess this is an answer in two parts: most pertains to a situation if Sammy had no problems at all.
The caveat is Sammy's problems. It sounds like he perhaps does not find other dogs very pleasant additions and a puppy would nag him CONSTANTLY to play, steal his toys and food, etc. If you cannot be there to manage that activity, he could seriously harm or even kill a puppy. Overall, sounds to me like he would be distressed by a puppy, maybe even most other dogs -- *maybe* an older quieter adult would suit better that didn;t want to play. So in relation to what is said below -- it really relates more to the general situation. How has he been around puppies? Does he show any pleasure at all in other dogs' company? Could you (as would really need to be the case) keep them separate from each other but together in the same area (eg keep the puppy walled off behind a playpen...).
If all else were equal -- I would say this for anyone considering whether it is possible to add a puppy to a work situation...I think if you have 6 weeks to dedicate to starting on housetraining, that might get you started but really for many reasons you'd do better with an older puppy. You could just reconcile yourself to working with either a litter box (in which case opt for a female) or pee pads. Housetraining will perhaps be a permanent issue if you can only get your puppy (barely) started with 6 weeks training. Of course you will have weekends then too. But a young dog cannot hold itself for 8 hours -- really only adults have that ability and it still isn't really ideal even for adults every day, but to be fair, again, lots would manage their dogs in this way.
Bottom line: I do think a companion would be a great addition for your singleton dog EXCEPT you have this special case of a health issue which does not make this easy. And yes: dogs mostly sleep all day but you would want some good toys etc (I think most Nina Ottenson ones are interactive with owners, however, and cannot be left alone with a dog though maybe there are some that are great for solo playtime -- kongs etc are good busy toys). If you can give them a good 30 minutes of walks/activity at least each morning and then when you get back from work that will be a good approach-- these are the activity times for dogs -- most dogs unless taken out, will simply sleep most of the day. I work from home and my dogs sleep 95% of that time (though we go out midday for a brief walk and they get about 4 walks a day). The big issue is really housetraining and lack of human interaction with a puppy but if you can give that much time while on your holiday -- frankly I'd say that is a better start than 75% of homes gives their new puppies. Most people I know who ask me for advice about getting a new dog or pup (of any sort) are people who work all day. I honestly do not think this is necessarily an issue IF you can set up a situation to manage and IF you recognise there will be some real difficulties and the problem may be more on your personal side -- the exasperation of a poorly housetrained dog and a lifetime of management and/or a very, very long housetraining period. But you know what? I have that already with two of mine -- an elderly dog (when they often have incontinence issues) and Tansy who was ex-puppy farm and is about 80% reliable but needs to be left when I go out in the kitchen where it doesn't matter if she pees on the floor (as she often does). It is not the end of the world and for me is only a minor inconvenience-- but for some people this would alone be a reason to give up a dog a d people regularly post to this board saying they or their spouse are ready to rehome their dog because of indoor accidents/inability to housetrain/etc.
I think you need to assess your home setup and what Sammy honestly needs/wants/, then of you truly think an addition would be a *benefit* to him, potentially talk to a breeder about potential litters and ages and the possibility of an older puppy perhaps that they have run on to show but have decided not to keep (this is common for breeders), consider if someone could come in midday for a walk... you would need to have an arrangement for the puppy to be returned if things are clearly not OK for Sammy and be committed to doing this if needed.
You can of course potentially make it work
but just don't let the thought of a cute new puppy (which even in the best situation, is always exhausting work!) cause you to idealise the situation or underestimate the serious challenges or the possible heartbreak of having to return a puppy after a few short weeks, which could be very hard for you.
I do think your priority has to be responsibility to Sammy's needs rather than what you would wish you could have under more normal circumstances. But I don't really know what he is like with other dogs and only you honestly know the situation.