crunches and situps are useless for runners. They work your abs which are fast twitch muscles that cannot really be used at all in distance running. If you do core, focus instead on deeper core muscles with planks (front, back, and sides) and "6 inches" holding your legs up off the ground. Never do russian twists or bicycles. You could do paloff press as well.
I would recommend seeing a PT at least once to actually identify your weaknesses/imbalances. Make sure it is a good running PT not just any guy. It will save you a lot of time, effort, and frustration. Read Anatomy for Runners or just do the tests in the back of the book before reading it. If you cannot keep a flat back with in a half kneeling position without feeling a stretch in your hip flexor, it is too tight. Stretch for 3-5min each straight after a run if this is the case at least 6 times per week. 80% of runners have tight hip flexors from sitting too much. Your glutes are probably also deactivated and too weak (again most people from sitting), so do glute bridges and other glute activation exercises pre run and post run. If you can't bring each hamstring up to 75º stretch those up against a wall for 5' every day after a run. Do not waste your time with any shorter stretches post run. Always do a dynamic warmup and if you have time roll before a run. Roll after runs and get your feet with a lacrosse ball. Do strength exercises for stabilizing muscles in your hips and glutes and core every day. Make sure you can balance on one leg with your eyes closed easily. Learn how to activate the muscles deep in your core an inch below your belly button by pressing your tongue to the top of your mouth and exhaling. Learn to do this without the exhale.
To answer your original question, one day off is always worth it. I have been injured for two months now because I did not do this. It will not necessarily hurt during a run but could still get very damaged with no pain. Just take a day off if there is any question in your mind. You can always bike or aqua jog and one day will not hurt your fitness but two months will as you probably know. I really do recommend that you read Anatomy for Runners and see a PT.