I applied for my AmeriCorps position and started in 3 days and I haven't had any issues at all with scheduling interviews this fall. But I was very clear with my site supervisor that I would need time off for interviews, so it's not like it was a surprise to her.
Every AmeriCorps position looks different. There are some, like NCCS disaster support that are 10 months long, very intensive and don't have a lot of flexibility. There are VISTAs, who are slightly less involved but still working directly with people. Then there are AmeriCorps state positions, which are often indirect service through working with non-profits, etc. These are the most flexible options.
Then again, n=1 so take the with a grain of salt.
TFA is a way bigger commitment and has way less flexibility.
However, the pay (living stipend) is lowwwww and you really should be committed to the project you are working on.