Does overstaying in the US have an adverse impact on attempting to enter Canada with a tourist visa?

Firstly I want to address the overstay, given the dates on your I-20 and visa are both still currently valid. Based on the comments on the question, some people believe that there is no overstay. This of-course is not the case, for all non-immigration visas (NIVs) you need to make sure that you continue to meet the conditions during your stay in the US. For example if you're working on a H1-B then you need to maintain employment throughout the validity of your visa, if you get laid off from your job then you have 30 days to find another employer to petition USCIS otherwise you must depart the US within the 60 day grace period. There are similar restrictions on F1 i.e. student visa that you currently hold, you need to be a full time student with the opportunity to work part time when school is in session or to work on OPT during your course or after completion. In your case it appears that you have dropped out from school, so technically the day you dropped out from school you went out of status. You do have typically a 60 day grace period to wrap up your affairs and to then exit the country.

Now that we've established the overstay, to answer your question we need to talk about how the immigration systems work. Dropping out of school will not automatically inform USCIS that you're out of status. This will only happen when your school informs USCIS and SEVIS will then be updated. I couldn't find documentation around when this is supposed to happen, this would depend on the school; some schools might do this immediately, others might only do this before a new semester. As you might know or intuitively infer, US and Canada do share immigration information. Now obviously it isn't documented if this process is realtime or if information is updated after a certain period of time. So the answer to your question based on this is, it depends. If your school has yet to update SEVIS then you may be able to travel to Canada without any issues, if however they've updated the system then it is quite likely that you will need to answer additional question before a determination is made to allow you to enter Canada. In theory, admissibility into Canada isn't going to be decided based on an overstay in another country but in the eyes of the immigration officials it may make you more likely to overstay your TRV in Canada and you may be denied entry based on them not believing that you intend to leave Canada at the end of the authorized period. I would personally think that there is a high likelihood of you being denied entry, unless you are able to convince the CBSA officials that you will leave Canada.

Lastly, I'd like to explicitly state that this is just my opinion based on my understanding of American and Canadian immigration systems. This isn't legal advice and you shouldn't rely on this solely to make any decision. I would like to also give you some advice here, I have no idea about your purpose of visiting Canada and am presuming that before you return to India you're planning to visit legitimately as a tourist since you're already in the US. I would urge you not to do this or to continue to overstay in the US, you should contact an attorney experienced in American Immigration system to see if it's possible fix your immigration status before you depart - Maybe to seek admission in another school or to re-activate your enrollment in your previous school with this time being considered as a gap even if you don't have any intention of actually completing your course. Departing with a clean slate now is going to be hundred times better than, leaving things as they currently are. You are a student and at this time it may not appear to be a big deal, but this can come back and be a nuisance to you for a very long time. Maybe after a few years you want to visit a western country on honeymoon, it can be quite unpleasant to be denied entry or if after repatriating to India you land a job with a MNC and traveling to the US for meetings etc are a part of the job role, you may find this to be a significant handicap.