If I was to implement a visitor queuing system for my website, where if visitor count is higher than n, place them in a queue. Would this have an effect on google's ability to crawl the site?
It depends on how you implement it. For Google to crawl the website, it must get a successful status and get a crawlable response, which usually means returning a 200 OK status plus some HTML back.
Now suppose you send back a 503 Service Not Available instead, it will attempt to crawl back later. If it gets them often though, the crawling rate will drop and possibly eventually stop.
Any actual error returned such as 4xx status codes will really impair Google bot from crawling the site and they will appear as errors in Google Webmaster Tools.
If you are limited in resources, you should probably let googlebot through and serve it content from a cache. Of course if the limit is bandwidth, then there is not much you can do about it.
Yes, agree with comments above. You need to think in a way to solve the problem so that users do not need to wait. As no one likes waiting.
Having said that if the core design is to let user wait after x number due to tech, resources or other issues then you may have an issue from SEO side.
Google expect either you let the Google bot to crawl or clearly notify not to crawl. If Google will not be successful to crawl every time then possibly you will have a ranking issue and you will get warnings in Google Webmaster Tools.
So, the recommendation would be to think hard about your implementation strategy have a clear approach, Yes or No for Google.